f rNa«i ?SpS8gS 1^

IM'

PRKLIMINARY INVEST I OATIOK OF THE KIXINO

OF A PULSATING ilR JKT

in A STEAIYSECONDARY AIRFLOF

-^

A Th«8l«
Subidtt«d to th« Graduate Faculty
of the University of Uianesota

Charles J. Burton
Lt. Condr., U.S. liavy

In Partial Fulfillswnt of the Requirements
for the Degree of
Master of Science in Aeronautical Engineering

August 1951

^d

• O** I \/*Ml

iCKNCWLKDGKUEHTS

. '.r "' •

Th« Author wishes to express thanks to Dr. Uewmn A.
HaII and Professor Thogws L. Uurphy for the^r academic aid and
counsel, to the Hary group and Patricia Burton who kindly as-
sisted in operating the equipnent and takin^; data, and to
Michael Shonberg, £• Kaar, and William Alden for Taluable sug-
gestions and material aid in construction of the test set-up.

Thanka are also due to the U.S. Na-val Postgraduate
LohoQ^ Annapolis* Uafrland, which sponsored the attendeno« of the
author at the University of Minnesota as a candidate for the de-
gree of Master of L.cience«

A j:i»j-

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AppndU 40

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TABLE OF COMTEKTS
t

Sumnary ••••• 1

Introduction ^... 2

The Statenont of the Problem 2

Basis of bolution of the Problem • 4

The i^pparatus 6

General Lasoription of Complste Apparatus • • • 6

The Pressure Sampling Valve •• 8

The Pulsator •.••••••• 11

The iir Plov System 12

Instrumentation • 13

Itiscellaneous Apparatus 15

Test Procedure 17

Test of Serviceability and Accuracy of

App8a*atus • 17

Tests of the Flow Mixing Region 19

Discussion of Hesults • 21

The Operating Limits of the Sampling Valve • . 21

The Mixing /.egion Flov Data 24

Conclusions and iLecomnendations •••••••••• 35

Bibliography 39

Appendix ••••• 40

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LIST OF TABLES

Table

I to X Pijlsatinc I-'low, Cycle of L^anic Pressure 43-52

XI to XIV IrynA^G Pressure Profiles 55-56

XV to XDC Lines of Constant ^"^ 57-61

qo-qs

IX Centerline Values of Velocity 62

XXI to XXII Nornalited Velocity P»-ofilfl8 63-64

s by I

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aairon ho tsij

0V-.Y9

G- ....

68 . *. . . ^

&8 . , . . »vIjeV lelqnflu lol anuO noi;fe*idilis0

smoufiT

Zi . An inveatigation of the mixing region of a cool iso*

thei'nal pulsating air jet in a steady secondary airstrean at
Keynolcis number « 41,000, velocity ratio ■ 0.5, pritnary velocity
200 fps, was conducted by means of a velocity survey of the

•»

region, utilising a total head tube, static pressure orifioe,

and a sampling valve, which by rotation and synchronisation with

I-

the pulse producing valve, applied a constant but different

pressure differential to each one of 36 nanometer tubes in suc-
cession, producing a standing wave of dynamic pressure of the
pulse cycle.

The pulsating flow nixini; region was compared to the
mixin^: region of a steady flow Jet of similar configuration and
found to differ very slightly, if at all. The mixing re;;ion
agreed closely with that defined by previous steady flow investi-
gations. «f«ff%tuM»ial.> ■^' ••»• 'r«

fi m-
The investigation was conducted under the auspices of

the keohanical and ieronautioal ii'ngineering l«epartments of the
University of Uinnesota in partial fullfillment of the require-
ments for the degree of Master of Science.

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- £ -

INTRODUCTKW ««t

Th» Stateawnt of the Problem

*r
Th« nixing of fluid Jet with surrounding fluid hat been

inTestigatod analytically "with experimental confirmation by num-
erous investigators for various configurations of flow, but has
always been limited to the steady flow oases. Based on Prandtl*s
mixing length cOTioept for turbulent flow (1) Taa nodified by
Taylor (2)], Tollmiea (3) and Kuethe (4) have produced and eon-
firiMd theoretical analyses, of the extent and nature of the tur-
bulent mixing regima formed by free Jets.

Two excellent sunnaries of isotherml and non isotherinal
air jet investigations are reports by Cleeves and Boelter (s),
and by Shapiro and Forstall (6), the latter report offering use-
ful empirical relations for the shape of the mixing region.

• ciflK< Unfortunately, the non-steady flow case in which there

exist pulsations of a random nature, and even that case in which
the pulsations are regular, have not lent thenselvea to analyti-
cal treatment. It is felt that statistical methods will soon be
brought to bear on the subject with productive results, but it
is also desirable that sup;;lenentary data be introduced by ex-
perinental investigations.

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otJwiJ' ;ioiuW ax e^;-. Toi'i v^BB^z-'iioa ©ret .xJ-'-^-^'S'"'-""^'^'^'^

rfoldw ni d8B0 iarii n©T» bn« ,e*ii;;*Bn mobnai « lo oaolimzivq &9lxm

do li&oa II X'.. di}^iiJ&is imoiiiit^B^L imii J'is'l ai ,,'i:>J:::jA ij

- '- 3 -

i- Th« d«»ign •ngineer of turbojet, ramjet or pulse jet

•ngina combustion chambers is oonTronted with a need for design

data concerning the nixing of fuel vapor and air under hijjhly

turbulent conditions, often times under conditions of regular

pulsing flow as in the cat^c of the pulse-jet en>^:ne, or when

resonant conditions exist in the oombustion chanbers of other

types of jet engines.

viLive

:^ — It has been found by Godsey and Toun^^ (7) that such

oonditions exist in a £;as turbine eonbustion chamber as evidenced
hy observed fliokerln£; of the flame front position at frequencies
in 6000 cps, 250 to 600 ops, and 25-60 cps regions • And Scur-
look (8) concludes that rou^. burning is due to random fluotua-
tions in the mass flow, caused by fluctuations In the pressure
drop which are in turn caused by random fluctuations of the frac-
tion burned 3n any cross-section; and that resonance or flutter
ooours when the period of vibration is the resonant frequency of
some part of the system*

It is felt that a study of the basio mixing problem is
a neeessary prelude to further studies involving actual combus-
tion. It is the purpose of this lnvesti£;ation, then, to show the
extent of the nixing region of a low frequency pulsating air jet
In a steady secondary air flow by means of a velocity survey of
the region.

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B»«ia of Solution of the Problea -:•♦» f ar

•oc^i levrstl or .

The approach to this phase of the problem is experi-

nental in nature. The axial velocity field oan be charted by
■aking a survey of the mixing region with a total head tube and
static pressure taps. The difficulties involved in measuring
non- steady pressures can be overcome, if the pressure variation
is periodic, by use of a sampling valve which presents an open
passage to a particular raanoDoter at one point in the pressure
cycle only and at the same point each oycle. Assuming no leak-
age from the tube during the rest of the cycle, the particular
tube then is subjected to a steady pressure rather than a vary-
ing one. Use of many tubes, each recording a different point
in tVie cycle then produces a standin^^ wave of the pressure pulsa-
tion.

Static pressure readings oan be taken at the ed^e of
the flow for all points within the flow at a particular cross-
•aotion. Prandtl (l) has shown and Tollmien (S) has confirmed
that the static pressure is constant across the jet within very
•Mil limits.

Direct comparison of the mixing region of a pulsating
jet and the mixing; region of a steady jet of similar strength
will provide a measure of the pulsation mixing region ss well as

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- 5 -

its relationship to the stmidy flow case, for this particular
ooafiguration.

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- 6 -

General beacrlption of Coppletc Apparatus

A schematic dia^ran of the apparatus used it shown in
Fig* 1. Photo^rai^ ^^ ^^® apparatus conponents are Fig. 3 to
Fig. 10.

The apparatus consisted of an air supply system oapable
of furnishing air to two floar lines which divided the air supply
for prisary and secondary air flow and which contained standard
A.S.M.E. square edge orifices with "radius" taps as described in
Bef. (9) for ceasurement of the mass rate of flow in each flow
line. The primary flowr passed through 2" standard galvanised
pipe to a rotating; disc type butterfly valve, which served as the
source of pulsations, from whence it vas smoothly p washed down to
a one inch inside dianeter brass tube and ejected into the test
section as a tr^e Jet. The butterfly Talve was separated from
the fteasuring orifice by a 2^ ft. by 7 ft. cylindrical surge tank
to prevent the pressure pulsations from travoling upstream to the
orifice and affecting it* acouraoy.

The secondary flow passed through a six inch I.D.
smooth blaok*iron pipa, which contained the neasurin;; orifice,
to a 22 inch by 35 inch steel drum which served as a plonum oham-

- a -

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- 7 -

b«r and which surrotmaed the primary flow exit line concentrical-
ly* The secondary flow was then exited from the drum into a square
"tell" which had an entrance dimension of 11 x 11 Inches and
which tapered smoothly to the 6 3/16 inch square test section to
permit smooth entrance of the secondary flow into the test sec-
tion, surrounding and concentric to the primary air jet. iiight-
een-mesh screen xas placed 14 inches upstream in the flow to as-
sist in getting isotropic small scale turbulence at the test
section entrance.

The test section consisted of an 8 ft. lon^- square
duct constructed of angle iron reinforoed, smooth ^ in. plywood.
One side of the duct was constructed to slide so that the total
head tube and static orifice located in the sliding panel could
be placed at any desired station, lonf;itudinally, in the test
section. The downstream end of the duct was opan.

The total head tube and static orifice pressure leadt
were connected to a rotating sampling Talve which was synoronised
with the rotating; btitterfly valTe so that a standing wave of
total pressure minus static pressure could be produoed on a bmnk
of U-tube nanometers.

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- 6 -

Tlie Pressure Jamplin^; Valve 'rKHf;tmT Amt

It vas desired to know the variation of Telocity, and

t«
thus pressure « with time in the nixing region, iyailable for

this purpose was a rotating pressure sampling valve, constructed

by £. £. Becker for his Master's Thesis (10). 1 sohemtio dia-

Iprani of the sampling valve is shown in I'ig* 2 and photographs of

the valve and its associated drive meohaniam and nanoKeter board

in Fig. 2-1) to Pig. 2-h. y^ paaea

ks described in iief. 10 and Kef. 11, the valve consists
of a truncated oone shaped rotor (4) irtiloh rotates within an outer
casing (B)« Two circumferential grooves, (C) and (D), have been
■aohined in the conical section. Drilled in the outer casing,
80 that they match up with the two grooves in the conical sec*
tion, are two pressure taps, (t) and (F). The pressure leads
from the total head tube and the static pressure orifice at the
test section were attached to these taps. An L shaped passage (O)
has been made in each of the outer lands of the conical section
resulting in a single hole in the face of the land. Lrilled in
the outer casing are 72 holes, 36 equally spaoed in eaoh of the
two rings. These ar situated to line up with the holes in the
lands of the inner rotor. The outer easing is restricted from
rotating by the pin (H) whioh passes through a slot in the sup-
porting base (l). The rotor is driven by a pully and the outer

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- 9 -

caiing is held up on ':he taper by « epring arrangenent. The outer
casing is six inches in dianeter at its largest and is tapered to
a 30** inoluded an^jle. It is supported by a pair of bearin^js and
pillov blocks whioh provide for eaey disassenbly of the tsItc.

The principle of operation of the valve is as follows.
The pressure changes are transnitted through the connections in-
to the two circuoferential grooves naohined in the surface of
the rotor and up through the L shaped passa^.ee drilled in the two
outer lands. As the oonical rotor rotates, the pair of holes in
the lands pass each of the 36 pairs of holes in the outer oasing
in succession, different pressures exist in the L shaped pass*
af.es as each pair Is passed, but if the rotor is in synchronisa-
tion with the pulsation frequency, and the pulsation, is regular,
the Bane pressures will exist in the L shaped passages each tiaa
the holes in the rotor lands pass a particular pair of holes in
the outer casino;. Thus, if connect:lons arc made to a different
U-tube manometer from each pair of holes in the outer oasing
whioh occupy the same circumferential position, the pressure dif-
ference as it occurs at the particular point in the cycle of
pulsation will be registered. Nith each of the 36 pairs of
holes connected to U-tube manometers arranfed in a bank, a stand-
ing wave showing the A^ at each 10*' increment of the pulse cycle
will appear on the manometer bank. Thia assumes that (1) the

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- 10 -

IsTel of the fluid in QAnooeters have a oowa<m reference level,
(2) tliat no leakage occurs from a tube« between successive appli*
oatioiiS of the Ap to that tube, and (3) t}iat no additional posi-
tive or negative pressure is produced by the dynamic effects of
the valve rotation itself. As will be described later, item (2)
is a source of error wliich can be reduced by rotating the valve
at speeds greater than 200 rpm and item (3) is a source of marked
error which only calibration can lessen in the valve's present
configuratl on.

irre frt^i^The valve was driven by a ^ hp, 110 volt, 1750 rpm,
AC electric motor throu^.h a system of two 6 inch variable speed
pulleys. An 8 inch pulley on the shaft of tue inner rotor of
the valve combined with these two variable speed pulleys afforded
a speed range of 120 to 370 rpn.

- ox -

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- 11 -

Tha ?ul«ator

The source of pulsations in the priaery flow was pro-
Tided by a 2 inoh diaaeter disc type butterfly val^e which rota-
ted in the primary flow pipe. The yalve completely olosed the
passage when closed, thus the air flow Taried froB sero to aax-
l«nB« The butterfly yalve was connected to the inner rotor shaft
of the sanpler by a flexible shaft and a 2tl gear ratio. The re-
duction ^ear synchronised the sampler valTe and butterfly valve
since one revolution of the butterfly valve constituted two com-
plete pressure variation cycles.

The frequonoy of pulsation was adjusted by the variable
•peed pulley system and was oontrolled during runs by use of a
•trobosoope to accurately attain and maintain the desired pulse
frequency.

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- 12 -

Th« Airf lowr System

thtt air iupply used for the te«t« iras obtained from «
per^ianent installation located in the turbine test oell of the
Mechanical En :;;lneerin^ 'Depart iwnt. A gasoline powered Lycoming
Model 0-435-T air cooled Army tank enclno, rated at 162 hp at
2800 rpm, drives a centrifugal compressor. The compressor is a
7,48il .rear ratio auperchar£;er taken from an Allison V-1710 air-
craft engine. The speed of the blower can be aeo';rately con-
trolled by throttling the en^jine,

A standard A.S.M.H. square edged orifice is mounted

upstream of the blower inlet to permit eraluation of the mass

nt

rate of flow through the blower and to {lermit accurate mainten-
anoe of a desired flow rate.

«aar* c»r»>p» i^.i^nm* ♦h<» isqoer*

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- 21 -

b«^auo« zl ftotllio 5 .2. A faiflbnacts A,

- i3 -

Inst runentat ion

prasa

rygtm^ n/'f fTiv^ ■'>" ^■Jrrr: sis'* r*^!*'

The total presaure was measured by a 0.028 inch O.D.

total head tube of the Kiel type, which has a vonturl shield
surrounding the tube tip to insure flow nornal to the 0.017 Inch
IaD« tube opening;. The pitot tube shaft was ^ inches O.D. brass
which was nounted in a ^ inoh thiok plexiglass plate throu{;h a
fktfJttrooT paokin^j; gland so that the probe oould be noved later-
ally across the test section width. The plexiglass plate also
contained a l/d inch dianeter static orifice. The plate was
Bounted in the sliding wooden panel of the test section so that
it oould BOYS up and down independent of and/or longitudinally

with the panel J thus, the probe could be positionad at any point

potas

in the whole test section duct as desired.

The pressure difference, ^, between total pressure and
static pressure was indicated on the U-tube Banoiaeter bank pre-
Tiously described.

The pressure drops acroas the square edged neasuring
orifices were measured with well type water-filled manometers.
The pressure taps froB the orifices were located In accordance
with A.S.M.K. standards for "radius taps", Ref. (9), the up-
stream tap bej n,3 located 1 diameter froB the upstrean face of
the orifioo and the downstream tap ^ dianeter from the downstreaa

-si-

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- 14 -

face of the orifice. The atatic preaaure holes wera ^ inch dia-
nater and free of burrs and reatrictitms with ali^^tly rounded
edgaa.

The static pressure level at the upstream tap was mea-
sured on the sane nanometer used to Measure the pressure drop by
clampicg the lead from the downatream tap and removing its other
end froc the nanometer, causing the nanometer to indicate r,age
pressure Juat upstream of the orifice*

The tenperaturea at the orifices were measured by Iron-
eonstantan thierrr.ocouples Inserted in the flow upsteam of tha
orifioas in acoordanoe with I.S.IH.E. Standards. Temperature
readings were made on a Brown direct indicating potentiometer.

Tl-ia orifices were maae to A.S.li.E. Standards and were
■aohined to an inalde diameter of 1.008 inchaa and 4.002 inohaa
for the 2 inch primary line and the 6 inch secondary linea re-

apactlTely.

ji^^. »-5a»a:

A oheok on the accuracy of the orifices waa mada poaai*
ble by the insertion of a maaauring orifioa at the blower inlat,
whioh panaittad a maasurccent of the total maaa flow to oorapara
with tha aun of the flows through the primary and secondary linea
aa Indieatad by tha other two aaaauring orificea.

r^ rr ^T77

i»A

. as-jfco

ic-

Hv": ft'tvr:;

lo Olfle

-•"IB -iU

-•1 «c

yj^'ifta

a«oiliio

^•n

fq iionf S ft^'* t«'^

, Viuv Lv' -j^-^^i

'tzmoq mhaa a.sv-

• Of

. aoo

diij no iio*ilt:« a

- 16 -

Miie«ll«noou8 Apparatus p thm -yrmwMurm

Flow Pipes. The A.S.M.E. code on fluid measurement
does not recognize the use of any pipe snaller than 2 inch I.D.
Consequently, 2 inch standard galvanized iron pipe was used for
the primary flow line and 6 inch I.D. snooth rolled black iron
tubing for the secondary flow.

Surge Tanks. In order to prevent pulsations from the
prioary flow fron affecting the measurino orifice in that line,

a

the orifice was placed in series between two 7 ft. by 2^ ft.

cylindrical tanks which served to damp out pulsations originated

fron either side of the valve.

c*- at— imy 4i«« tyfs biHarfiy

^^ Since the pressure variations in the secondary flow
line, caused by the pulaationa in the prinary flow line, were -i
M«h staller eompared to total flow, and since the secondary flow
orifice had a dianeter ratio of 66 2/5 per oent it was felt that
Ihms capacity was needed to insure steady flosr at the secondary
flow orifioe. Therefore the only surge tank used was a 22 inch x
S5 inoh steel drum placed between the possible source of pulsa-
tions (the test section) and the orifioe. This drum served the
additional purpose of a stilling chamber to aid in establishing

a smooth isotropic entrance flow into tho test section.
»t rpeseoepti

fre^meaa^.

' di "

Buctanacc-; h e^

••' ij

.C.I rfofli S ^«.i:^ T»II«a8 &q£q X^» "» •»" •^'^ osiixsoosT Jon ^u

,o'> hi9*y' 3SW »^'tq noil besiftarlBS onBbns.+a xionf S ,^^1 J-nenpeaxKiO

^oTx un.v. .....loi dc^oorai . ..-^ ^n-.r n b-=' orrJI troll vttr^rir v.:

j.« Xjj „., .^-^ y Q^j. j,r,f^^,-t©cf ««?"n»8 PI f bftoslq atrw ©oHino ©rii

noil •it«L;iou«ii 3ilw oo;u3 jrta ^vtoLI x^::o^ .- ;r-iiiLv;. u -...ilsiifB riooa
;t«rii ;tIol asw ;H :^n80 loq S\S 36 lo oi:^ai neiamflib a bad ©olll-to

viAbnooea "'-f-* <'^ "•'' T"' v'lasita onuan^ oi .bsbssn saw \:;tJto«qao aaal
^x ifont SS a aa» uaau /Inac^ o^ija \ifio D;i:r anuio-ion. .ooitcio n-oll

-aalucT lo aonuoa sidi 2Boq o/iJ" neoir*ad bsoalq rawib leads rioni t.S

::J-a© Bi oi» OJ* Tecmano ^niliija t. lo saoqiwq imicxJiDoa
+ orf* o:J'fli woi'» oonand-na oxqonrtoai ri*o««« a

- 16 -

Throttling Orific«» In ord«r to build up the pre8«ur«
l«Tel of the air supply to the primary line so that a greater
range of air flofw control Blight be obtained, an orifioe with an
area ratio of 66 2/3 per cent was placed in the six inch line
Just downstream of the take-off of the 2 inch line. Then Just
ahead of tho 2 inch line entrance to the first surf^e tank a (;*te
Talve was inserted in the line to pernit Tariations in the pri-
■ary air flow velocity. No provision was made to control the
secondary air flow except by variation of total flow through
changes in blowor speed.

The f'ulsator. The source of pulsations in the prl-
■ary flow was provided by a 2 inch dianeter disc type butterfly
valre which rotated in the pritaary flow pipe. The valve com-
pletely closed the passage when closed, thus the air flow varied
froB zero to naxinum. The butterfly valve was connected to the
•ampler rotor shaft thirough a lt2 gear ratio. The reduction gaar
synchronised the sampler valve and butterfly valve since one
revolution of the butterfly valve constituted two complete pres-
sure variation cycles.

The frequency of pulsation was adjusted by the variable
•peed pulley system and was controllod during, runs b. use of a
stroboscope to accurately attain and maintain the desired pulse
frequency.

- 31 -

anfl r nl '>f»«»«»In sew ol^tBt «ei»

•d-^j • a iV« ;tBiil art* O* ©oneis^na »ixli rioni S diij lo utt^dB

-ft.-, o.i:t nl znot&BiiBv ttiaifiq of arrli ^ »«» ©▼!«▼

fT^it^-l -i ! a,^i-> ■> p f ?•, "rt^flsw*"'' :'.nnf

~j . \Jk7_..i'-'

-^■.jT: "; ! ji.':j U'/.J -'•-

... - J/X«V Y^"^''"^"*"" '^'''' """' '•<■• ' *'''I'"V.-T

. 3 o i ;> V3 no X J A i tmv itiaa

•idattipr »rid y/i b»rr»jjf;b« 2«w nolctaaljjq Ic 'etl o<i

»fcii/<, DJ'liuaL, yil' .:zBw;ii3-!: -T.B ai6.w'« \^j.ij ;.',-iir on i. ^-

yt ..' t»u ' ' 'J jt *

njp»i*i

- 17 -

TEST PhOCfiUJHK t^kj

T«st of S»rTie— blllty and Accuracy of Apparatus

After the equipnent was assembled, all Joints and pres-
sure leads were checked for leaks. The samplin^^ vaWe was dis-
assenbledf inspected, lubricated with a mixture of SAE 10 motor
o) 1 and "Molykote**, a molybdenum sulfide dry lubricant, and re*
assembled. A spring pressure of a fixed amount (that pressure

which gaYe a spring constant of ^^^ , ■ gOO t- ^ "** *P"

•020in* in«

plied and maintained for all tests.

Next the Rsnometer bank connections were checked for
leakage by applying; a Ap across one air passage of the sampler
TalTo and then rotating the valTo ten degrees to close off that
passage, iiince the tsItc leaks only while rotatinj^ this i^sto a
ohaok on the pressure leads from the tsItc to the manometers and
a check on the proper assembly of the TalYe. 1

The valve was then operated through its speed range
to check for overheating or other malfunction.

Mart, with the engine running the ^ate valve was ad*-
justed to give the desired ratio of primary velocity to secondary
velocity of about two to one, the rTirary and secondary flows

wineMvt«r kmmk m.

• rr -

Jn')'

•e«'sq ba» 9d:

10 ja*'^ 0-

"\'.,'r.

3SA ««w p» e/iJt i©crlA

. !»c .:>«

1 B ••»■/■;

.«7aei Xi« -Wi

-7»8B«

'•q

.« »v .ioT •Xl.iv >{Ij«o Br:(«»X btI«t ori;t e

box BUVTtiMefiM: oAS ot •▼X«t ori:^ ■oi'^t tbt^L -'•Tv»a«rrr ««f+ rr;^ "ssrlo

9yi»n bt'

.noiionvlL

•ba •■« vrXarr aia:^ ar.

v*t«!j inn*:

nin anl^iisa id

- 18 -

b«ini: about 200 fp6 and 100 tps , re8pectlv«ly» The system was
checked again for leakage. The effectiveness of the sur^^e tanks
was then checked by varying pulsator rpm and noting the effect
on the manonetere connected to the steady flcm sections* In tt^e
range of 200 to 300 rpn no evidence or pulsations reaching the
steady flow section was noted.

The soouracy of the neasuring orifices was checked by
oonputing the flows in the primary and secondary lines and coB"
paring their survs with that flow measured by the orifice at the
blower intake, uood agraanent was found. .•/.< ..^^^^ . o'

too

The effect of the length of the tubing connect in^ the

total head tube and the static orifice to the valve was checked
by comparing the reaciin£;8 on the manoneter board using two sets
of pressure loads, one set with the connection as short as pos-
sible, the other with 50** leads. Ko difference was found for
these two lengths, consequently the 50" length was used for all
readings. This was ex^Mcted, since tho natural resonant freq-
uency for a 60* tube with (me end open is on the order of 4000
cycles p9r minute and is higher for shorter lenf;th8. The tubing
used was 3/l6 ID, thus not so small as to introduce capillary or
extreme friction and attenuation effects.

awnrm^ Vo drifting or pulsating of the water eolanns In the
Manoneter bank was observed during any of the check rims.

- 81 -

MV iae;t«X8 e.'fT ^\L»rt&99qtmi ,tql 001 bne aql OOS rfuocJ* era
onr n : rmeT sr jq 1o •onabtr© en nqt OOS o# COS "io B^aat

-v xr.'-t'SCa'a

' 4*\Ca O ' «! ^ ^^

bs'citn\o ajiw evlenr M(i o:^ bne f*do# ~'B ' c to#

IDl Lruc .abaoX "OU ni.;w lonto #0.^ t»IdJ:a

lie to^ im. 3r 'f ,-f-I "06 orf:? vit^ocnsanor; . »ff-*^n»I ow;f •••di

-pail -rflAncaen ieiuj*iu ;^ :t ,JU«j^uo».|X© tfew airfT .£,)flfb»»T

C<X)* "^o nebno ed* oo al awio bni» -jno Aiim 9dui "Od a 10I yorfu

• a^a«ll* n4tiBunB&iM bna nc o.T)9*i.^xft

.Bum ^oarfo Mfi ^o vn* n'-i::b b<ivt«a<fO SAW ':itaArf ^•^woonHi

- 19 •

Teats of tho Flowr fcilxlnf^ liegion

Before starting the test rxrns* the engine and Talve
were run until fully warmed up and running C(»ditions were stab-
ilised* J|»ta»«i.

To expedite taVing readings, a large sheet of paper was
placed behind the tubes of the nanometer bank and the water col-
ucm heights marked with pencil. The equilibrium positions of
the water oolunsis was narked on each new sheet before the run.

'« To obtain and maintain the desired pulse frequency of

250 rpci« a stroboscopio taohoaeter was used. A revolution tern
counter and stopwatch was used for initial setting of the strobo-
tach control since its control dial was not calibrated to the
desired degree of accuracy.

>i Control of the airflow was siaintained by throttling
the driring en^ina, using tha prassure drop across the primary
flow maasuring orifies as a reference. This -value could be nain-
talned constant to within 0.2 in. of water with little difficulty.

The initial run was a calibration run, tnade with the
sampler Talve rotating at 250 rpm. For a series of known steady
flow values of d^oianie pressure, "q", (total pressure minus static
pressure) ranging from 5 inches to 16 inches of water, water

- ei -

avX«v bam enl^an
-<fa;t£ 'J bwatBir - Xi;trai mil •

at \ .besu 8«w ne ^Rqi OdS

-oc' 'i?»:t'nj.TOj>

^lUOOB lO 99' Sib

'Oft ffOlh f^TfrtBSSTfT 3di •"

-n'i« ■ 'i '34... ev sc'M .f'' ■ . : 1 E 3ii jjai!; • ■ > - wcfit

.;T£ S.C aiif^-fw . 0^

.tin aol&miQ imo a sew hot X»li-inx sHT

im te amiont bi o& a- aasiq

- 20 -

le-7ois for all tubes In th« nmomoter bank were loarked for each
■q" value. Other calibrations were made later in the tests for
tht purpose of naintainiOj:; an accurate calibration of the Talve.

The pulsating runs were then Mide by eoAneoting the
butterfly valve to the sampler valve and markin^: the water levels
of the nanoneter bank tubes for each probe position. The trav-
erse consisted of readings taken each 0,1 inch starting beyond
the noszle center line and continued through the nozzle centerline
position to a distanoe of 2*5 inches from the centerline* This
was accomplished for a series of stations cosunencino at the
nozzle exit and continued to a distance of 39 noszle diameters
downstrean.

For comparison with the pulsating flow tests, similar
traverses were nade with the butterfly valve disconnected frotn
the sanpler valve and in the full open position. Hare, two
traverses were oadc. One was made at a prinsry nuiss flow iden-
tioal with the pritnary mass floa existing durin{^ the pulsating
runs, 80 tliat the average velocity from the nozzle sliould be tlie
sasM in both conditiona« The other traverse was Bside at an ar-
bitrary value of flow such that the q at the nozzle centerline
at the exit was the sasM as the q at the peak of the oycle of
the pulsating runs* (saAta* >■>« ^»r-y

• cs -

► V-t.'

ano i A ■•■ f

nt.'^ia&nitm lo : «ri:f

.1 TfrltesCirr

-.3 9rf^

-•M ra fp. o^sR aaw fit Mh>t

- 21 -

L. iilQM OP E2SDLTS»tr^^ ♦>«» re*cr «nd

The Operating Limits of the Sampling: Valre

WoBg (11) dtserlbet in sone detail the limitationSf
oep«biliti«8» end idiosyncraoies of the sampler TalTe. In brief,
the major aource of error is leakage across the vsIto whioh
Taries with the pressure differential applied across the ^alre,
the direction in whioh the Ap is applied, the speed of rotation
of the valve, and the spring pressure which holds the outer cas-
ing against the rotor*

rotor- ^r,A ','/• «« im' 4 tmr fih9mm iMrtl«ttle^ %**t

The speed of rotation of the Talve affeots the lealcaco

in several ways* First, it deternines the temperature of the
valve wVdch varies the viscosity and sealing power of the lubri-
cation film. This establishes an upper limit of about 300 rpm
beyond which the valve overheats rapidly. Low valve speed per-
mits excessive leakage by proloneing the time interval during
which leakage from the valve can occur between the successive in-
stants when a particular nanometer tube is subjected to its
particular Ap at its point in tl.e oycle. This places a lower
limit of about 200 rpm upon the vaivt. Most oritioal are the
dynamic effects of rotation. The valve rotor is not supported
independently of the ou'er oaainfr but ratl.er is supported in a
■anner similar to a Journal bearlr^:; and as in the case of such

- IS -

avIflV ;^nilqgfl^ arid" "lo e^tiatd ^ni&MisqV »riT
,'ieiitf nl .5>Tlftv lelqnwa atii lo aoioBnonxeoibx una .s-^i .;^j j. rjsq»©

aiC^f lo •rw;t«nsqra©.t srfct aenxcnsiefa &L td-sic. .a^aw I«n©v»8 ill
-Itdr'I 9rf:J to •j-'Voq *2nil3'?3 bna vl^aoa!^ 9.''+ 5t7t-BT .it;'-^'^ <^tIot

-n»q b««q« avX«T woii ,'<(Jibi<]Bi »do«r<t9vo ervXs^?- •ri;f jir/fTw bnox&d

Bil oi fao a «i •di/^ to 1 ifll L'O f J-f «^ 0 n»riw 3i'n»;fa

add- B'i« Ifli>i;Jiia >.r ^ i^Kit CCS d-«od» **© ^iwll

be; ^H af to.fon •riarr •riT .aoi.tsdon to - • ofnanyb

m fit hm *■-{(>! rr-.'- -f<^'»Tt 4rfr' .r.?.^r.,rv -fo /' ,-.,)+ -^z) '^X;trr«»bpf»q»i»n2

.(Oiis lo »<»«M> wtJ ni •ta©J X«muoi, w od- laXxola -tnnaaa

- 22 -

ft bMiring* rot«tion buiXdi up an air filn between the rotor and
casin^ and « circumferential pressure gradient is established

i^.ioh is a function of the speed of rotation.

jr i.* ■

The TalTe is thus aeon to be very inflexible in its
present configuration. D.xf»^y9r, by reuiainin;; within the limits
dictated and by remoTing the maximuTn number of variables it is
possibloj by calibration, to remove most of the error. Conse-
quently, for this test a constant sprin^; pressure was applied,
■ constant rpa was used, the pressure leads were attached with
the lower pressure always connected to the narrow end of the
rotor, and the valve was oalibrated for these particular test
conditions by applyin^j a series of known steady Ap values to
the rotating valve and narking the readings of the manometer
tubes. From these readings a set of oalibraticm curves over the
range of 5" to 16* of water were plotted and found to be almost
linear, as indicated by ffon;> ?!>;• 16 is a calibration curve in-
cluded as an example. The other calibration curves arc not in-
eluded sinoa they apply only to this very particular combination
of tast conditions.

It was found desirable to run all the actual flow tests
during the same test period since the calibration of the valve
changed from day to day as the amount ant. condition of lubricant
and other factors chan,';:;ed. Check runs made on other days re-

- ss -

h*^

a;H zs.

•KJ

- y6 t-

-B^

8^

in*-

-es-
quired that n«w ealibrations be nade.

The need far extrene care in controlling; the operation
of the sampler valve. I.e., the necessity for babying it, the
necessity for continuous reoalibration, and its inflexibility,
gre^Jtly reduce the scope of any testing done with it. The lati-
tude of possible test conditions Is narrbireS'lrjr' these lliai%«*»'**
tiona and the tine consucaed ir. obtaining;;;, reducing anc recheck-
ing data is enornous. Nevertheless, it seens to be capable of

ton «V

producing reproducible results within its linitations.

piu^ii»i«r .

i.'y

1^/* +2 .-,-,.-jg(^ ^f. rl*v nelqfflfta arid" ^

- 24 -

The Mixing &»gion Flam Data

For the purpose of definition, the nossle exit is taken

aa the ori£;iQ of ooordinatos used in plotting the data. The dis-

taxKje alon^ the nossle oenterline is denoted by iL poaitiTe dovn-

D

atream# in noxxle diaueters. The lateral distance froa the aos-
zle oenterline is 2L Thus y « 0.5 is the boundary of the noszle
and X • 0 is the atation at the nossle exit.

IT

T>ie value of 250 rpn used in these tests was arbitrary*
prescribed by the limitations of the sampler valve, it not being
practicable In the preliainary inveati^tion to consider the
effects of pulse frequency as a paraneter.

The foTB of the pulsation wave was not controlled* The
butterfly valve produces a flow varying fron sero to naxiiaunt of
a form sotnewhat sinilar to liarnonio wave shape.

The data is plotted in terms of dynaoiic pressure,

1 0 u2

q s Pq'Ps * tg> ' • iiince the quantity q is proportional to the

£o

square of the velooityc ^t shows pressure variations more dis-
tinctly than a velocity plot. Fig. 17 in the appendix is a con-
version plot of q to Yelocity, at the test conditions. For a
ratio of q values, as in Figs. 14 and 15, no conversion is needed
since a velocity ratio equals the square root of its correspond-
ing q ratio. Key velocities and velocity ratios are indicated

- >s -

-8

7 «o : I

:'rft

a

-ton

*.J

a

lo ar T ^<rf DedlnoBt.i

■'aw noXvBiijq ii-L*

ti, iV-xi' o;

1 fl

-not- * vXi«ai;f

be H .»- r p 1.

I ^^nl9

ir*

- 25 -

,Mn mo«t plot*. — i-v-^ ...««« ,,,4.v«i vj. -«ul4

Fig. 3 to /it;. 12 aro plots of the dynaaic pr«88ur«
▼•reus oanovieter tube« which is, in effeot, • standing-, wave of
the dyoanic pressuro cycle produced by (me cycle of the butter-
fly valve. The butterfly valve full-open position corresponded
to that position of the sacipler valve which indicated on tube
nuober 27. liowever, the peak of the q cycle is seen to occur
•o«M 110° later in the cycle* at about tube 2. At 250 rpm, this
corresponds to about 73 milliseconds delay betweon the produotion
and recording of a particular value. 7he delay is a constant
value since the standing wave showed no phase shifting but held
its position very steadily. The conplete cause of the delay
value was not ascart^ined since it amounts to an average velo-

city between butterfly valve and sarapler valvo of ..t. — i-1 =

.073 sec.

86 ft/sec. This is nuch less than the velocity at which tha
changed ratio of P(>/ps due to throttling Bd^bt be expected to

travel and very nuoh !••• than the local velocity of sound, at

•• w«a tour v***!^

which approximate speed snail pressure variations would travel.

i possible explanation is that the major portion of the phase
difference was due to the nature of the production of the pulsa-
tions. It is poasibla that the peak velocity through the butter-
fly did not oocur exaetly at the full open position. If nost of
the reduction in aasa flow occurred when the butterfly was within*

- 3S -

&9^SS £SO

9V

i';.--rtT'f: ■0':r«r:vL 'if?;*

:/ :^v -ii'l

.•"08

/
si

"file rjsJXI" 01109

i

leool ^ Yitav bne Xot«*s#

^i'

- 26 -

o
■ay, 30 of the closed position, then the mininuia velocity would

occur when the nass flow «a« at a low level and the flow area was
inoreaaing, as at the 45^ to 55^ position beyond the closed posi-
tion. Similarly the peaJc velocity would occur when the noass flow
was at a high level and the flow area beinc reduced, as at about

the opposite part of the cycle. This would place the peak velo-

o
city at about 60 past the full open position of the butterfly,

or about 100 past tube 27, i.e., at tube 1 of the sampler.

The important fact relatin- to this invest! gat?. on was

that the sampler measured a standing wave which did not drift

.tent
or pulsate.

.e^d iT"i — -r**-- hac on be«^-

The wave f orra in the pulsatini; Jet is seen to be fairly

l^ciBlar. The scatter of data points is less than was expected,

and curves wore plotted throU(!;h the points where eviclenoe of

cyclic variations occurod so that resonant vibrations, if any,

or other oyollo irregularities night be dlsoerned. However, no

oons latent evidence was found that i|Hpa:thatic vibrations were

introduced into the systetii as had been the eaee in the work of

Becker anu iTiong.

,:•,>•»* :lj5^V<ft * »*•.«• \iO«lA mhatr tn«'

jihase 1 At the trough of each wave there was evidence of rapid
prassure irro|?:ularitie8 whioh it is believed were associated with
the flow through the valve when the valve was very near the actui

- as -

0

3 -).■.«■ O.t

woll 33«i »dt n©fiw luoao blyow 'i;fxool3v .aoi#

»vi'ino;^d-''i

-t ^j5 3sq 001 iuodB TO

,YfJ« ^i tO!TO?+ ^:>3«T .^iif^ ^00 a«oI*«lTflv olXov/0

T-^ .-r.+ i'i

»'<■

o8»o orfd^ n*; 3 •/<:f od^

- 27 -

oloaod position. •^^■^■■yl< * yMi^*^*

Pressure pulses -were transnittod to the secondary flow
region, even at station i « 0, causing a q variation which aver-
aged 0.5 in. of water. This was transmitted to the secondary
flow outside the jet nixin^; region as a variation in static pres-
sure. To confirm this, cyclic measurements of p^ - p^tm "^^
P« " Patm w®re inade at 5. = 0. The value of p, - Puto *** ^o^nd
to vary from -0.23 in. H2O to -0.68 in. H2O, a total variation of
0.45 in. H29.

The Kiel tube would not have been a suitable instrument
for total head measurements had the flow configuration been such
that fl<wr reversals occurred. The check mentioned in the previ-
ous paragraph' showed t}iat total pressure varied smoothly froD a
value of about 15 in. 1120 to a minimum of about 9 in. at the
troUijh of the cycle, at the notzle center line at 5. - 0. The nin-
imum was about 5.7-; in. 1120 at the edge of tho Jot and about 5 in.
lUO in the secondary flow. At no time did it approach zero.
Thus tho possibility of flow reversal was discounted.

Curras for suooessive £. stations show t}tat a slight

D

phase shift seems to be occurring as the flow noves downstream.
The peak of waves for station ^ » 12 and beyond occurs closer to
tube S than tube 2.

-«.-

*t.

iiC

aai*i

91

K^a

« »r

rt-rn . '

,0- o;f .

. C gii • A ■

^&1 .. lO't

-«■ J eXsii

j ojx ^n •waxi. VI i mvt ai O^ii

L i\. ■ .i\; J.C8W3 .r.iiis j?_Hii.-i

- 28 •

riMliitv*' ' Fig. 13 and Pi£;« 14 are oross-plots from points from

tubas 2« 13« and 17 in the earlior curTes and from the steady

flow data. Xhey are profilaa of d^nrvanlc presstira showing the

Tarialicu of q with i. and with <L • The above mentioned tul:>es

were c}.osen so as to have profiles of the peak, the minimun,

and an intermediate portion of the cycle. That Intermadiate

value was chosen which l^ad a q^ equal to that of the steady

flow traverse which Jiad been made with a primary nass flow equal

to the prinary mass flow of the pulsating flow. This permitted

a direct comiwirison of a pulsating flow and a steady flow which

r

had the same mass flow and same average velocities*

i".^ It is noted tlat due to the inability to control thtf

sacondary air flow and the f)sct t^iat less blower speed was neo-
•ssary in the steady flow case to produce jdantical mass flows
for pulsatin{^ and for steady flews « the secondary flow was less
for the steady flow case. rov/ever« the change was small* the
ratio of aeeondary velocity to primary velocity bain<; 0,45 in
the steady flow case and 0.53 for pulsatin;^ flow, the ratio of
0.5 having; bean initially selected as the approximate value de-
aired for this invest 1 cation*

PlC» 14 and ri-^, 15 make it aeem that the velocity pro-
file of the Jet at the nozzle exit was not very flat. However,

nndui t> -.ri svuuB

n

■Ulif

.' 10 aOBl -) M

■i woll aajsa lacflds o

fMarr' -"r-*

<« iao

•3 a

-lecfa »'

a;
^ of:*rt

j>oIev

vf

&» :,

>aao woi'l '^odttJB aik* tc'

oictjn

x;XIa

•n-

ioli beiic

- 29 -

r«a— bwin^ that this a plot of q rather than velocity, on* sees
that tha correapondlng Teloolty profile would ba auch flatter.
The ed(;e valocity, if cotaputad, is seen to ba 7b% of the caxini;m
Telocity, vhich is flatter than the so oallad laminar flow pro-
file* Laninar flcar was not desired in this test, and with tha
distttrbanoa created by the butterfly and the existing £e3rnold8
number of 41,000 the primary flow is distinctly turbulent.

The profiles show two thin<;8 clearly, that a marked
similarity exists between the pulsating and steady oases, the
pulsatin- flow having a sli^-^htly flatter 5nitial profile, and
that the profile In each case showa si^ns of approaching tha

flat condition at about £. * 21. At this station, tha ratio of

D

tha raaxiauia velocity to secondary velocity ist

«o/us

Pulsating, naximuB v* V 1*20

Pulaatin^;^ niniraura 1.15

iatari Pulsating, interiwdiate ....•• 1.12
Steady, interir.adiate 1.19

ly station — » 27.^, the ratios had beconifai j^'^ orw th\M

h

<^iadiar: Ptilaating« sttzlnun 1.10

Pulsating, mlniauai 1.10

Pulaatlnc, intariMdiate 1.06

Steady, intermediate 1.10

By station «•- ■ 39, in eaoh ease, the velocity profile
aaa not apparent to the aaasuring equipment. This is not in ao«

es -

-o-w; wo.

b»IIfiO OS i^d-d-flii ::t iv >ol9T

arid a lo afi;.i« bwc eliloiq o<^vi d^«.<i

C .

Sl.i

2L,i .+3

;©«ooecf barf aoidai arfi .d*VS » -• no'^s^te

a

8"\o"

c

»>• n.i ,€£ « ij ttoi*B:^ii ^{^

o& :hic-(aqq« u^on •■«

- 30 -

oordanoe nith the work of oliapiro and Forstall (6) who found that
for staady flow a "slope coeffiolant", a measure of the nornal-
isad profile slope was constant as far downstroam as 140 dia*
Meters* However, sinoe velocity alon^ the axis beyond the core

of potential flow decreases with increasing r*, nore reliable amd

D

sensitive neasurin^^ equipment than the saeipler valve will be
necessary to carry the investigation further downstream than was
done in tris test.

tiespite the fact that this investigation was funda-
■•ntally concerned with the direct comparison of a steady Jet
and a pulsating Jet having identiwil configurations except for
steadiness and non'steaoiness, it was desired, for purposes of
•valuatin,-;; the type of steady flow actually attained and eval-
uating the accuracy of neasureneat* to compare the mixing ration
characteristics with t:iOse defined by previous investigations*
One of the nost useful presentations of experinental data and
•npirioal relations for jet flows of the nature present in this
investicstlon is that by Forstall and Shapiro (6). Anong their
findings are that*

^Iti*::'^ (l) All noriaalised velocity (and oonoantration) pro-
files tiownatrean of the core of potential flow have strikingly
similar shapes which arc substantially independent of fL . fur-
ore, these shapes may be represented rather well by several

- OS -

-Xm '-A.!-! 0.

nlttl.

lO^

il«T

K i •-■.! WVi.

arr

•ioiir<o u^ m bsm

at , - 9ri.t ■

lis

tmvmf

- 51 -

Rftthenatioal expressions* a cosine curve beinp; the most similar.

C2j Beyond the ena of the potential core, the value
of velocity (and concentration) varies inversely with x, irre-
•peotive of the velocity ratio, A ,

CS) SosM esipirical relations based on their exx>erl-

aental data arei

(a) The x^ value for the end of the potential corei

I)

L » 4 ♦ 12 A

(b) Velocity decay cGnrnstreaci of the potential

s*iT*r core, (x -^L)* *^ ■^'

D

A comparison of the experinental data of this experi-
toant witli the above empirical relations is made 'n Fi^> 14-c and
Fig. 14-d. Very close at;reeticnt «as obtained with the enpirioal
rate of velocity decay, indicated by the lil slope of the lo^-ar-
athmic plots. The exact actual position of the end of the po-
tential core is of course indeterminable experimentally because
a transition region exists rather than a sharp boundary, as in-
dicated by the lack of a sharp break in the experiaeatal plot.
However » the approxinate position oan be found by continuing
the straight line velocity plots to thialr InberEections. This
produces an '^L" position about l.b dianeters less tran the em-

- IS -

•1-te

twvm la

1 '

-T/

'^n

.A ^

^ tot it («)

A SI 4 * = .1

:(a^ x} t«lO0

•■1 M ,

-leo i2tr Iv

■>ia

-Tn/ io'i

•< S.+

>^ f>'

- S2 -

pirical value for the steady Jet and about 2.5 diaineters less

for tiie pulsating jet* tliia is ooneidered good acreenent*

b< «* ore m^

The ▼elocity paranoter *— was chosen to reduce all

plots to the same scale, and to eliminate the effect of dissimi-
lar secondary flows. This indicates the degree to which the Jet
retains its orij;inal excess of velocity oTer the secondary flow,
a Talue of """a = 0 thus indicating ooc^lete velocity mixing.
A sinilar paraaeter was used for the q plots described later.

«.«—«—.. To compere shapes, the profiles were mace dim©nsi<m-
less and norcalised oy plotting u-ug versus £. . kihen fully
normalised in this Banner, the profiles (Fig. 14-49) at iL ■ 12
and — ■ 21 (downstream of the potential core) are seen to be
almost Idsntical at both stations for the interswdiate value
steady and pulseo flows, except for a spreading near the baee
of the profile. f'orstaLl and Shapiro, in tl.«jir more carefully
controlled experloent, encountered the spread to a lesser de-
gree, it be in,;; caused by the poor exper intent a 1 accuracy possi-
ble in deternining (u-Ug) near the edf.e of the Jet.

Other profiles could not be checked because those at

— less than 12 were within the potential core and those at 5.
» D

^eater than 21 offered too few distinct po5nts for a valid de-
temination of r^^. However, these two profiles arc considered

- SE -

«^. , ,1 -3 enBc

• isiAl betffioaoo 8^Iq p ©Hi tol I»««B a«w i9&9mBiaq itdimla k
ebmi ai9W aelilotq 9di t«eqMt8 eiBqmoo oT

a

atf o;f Rasa eiA (stoo Iflid-nA^q eH:t lo aamt&uamoh) L^ * -^ bam
;)«'S48 A lOl •i<4i>*>xv «a»cl\L oeaLuq ooh ^OBa&u

jOb ifl:txniC7 rnoqxe ic ti »o«lg

X X

a

-•b briar « n we't ooi DoiaTtlo IS uui^i iB^fimt^

- 35 -

the nost significant sine* the unnorinalized velocity profiles
differ markedly lj«tween the two stations^ the profile at — •
being that one at which definite flattening- of the profile, is
first observed.

For direct conpariaon, a cosine curve is also shoim
and glTes ^ood agreement in tha region where experimental ac-
curacy was good.

The previous coaparisons then would indicate that tha
experimental accuracy of this investigation was better in the
regions where larger pressure differentials being measurod than
near the edges of the Jet wliere the pressure differentials wera
snaller. Kowever, the ^^ood agreement of the data with that of
previous investigators indicates that the accuracy of measure-
Meats was reasonably good.

To actually picture the Jet mixing region, Fi~. 15-ft
through i'l^;. 15-e were plotted. These plots delineate lines of
constant q, utilizing the parameter °~^ .

Tha follow! n.: table, from values in Pig* IS, compares
the points at which the center line flofw might be considered
nixed to various degrees*

- 55 -

(Si:

>4f»«ai*! r '• ".r- -k (•<''v w ,>. r

^

^8 ri-stoa mAi

ono «-*:*:.

o *«nn

Gd~ vu6^;JO

ariT

-e-iyasa: i

:>ui} VI J.

aaf:

- 54 -

1 Value* for lUxing 85^, 68^ aad 55^ Completed:

D

Pulsating;* naxiouD
^Isating* minimum
Pulsating, intermediate
Steady, Intenaedlate
Steady, maxinn

u-u

«o'

■«•

0.15

0.32

0.45

xA

x/D

Vu

35.0

24.5

19.0

37.0

27.0

18.3

36.0

24.0

18.4

35.0

21.0

17.1

34.0

23.0

16.0

Prom the above, the conclusion mi^ht be drawn that the
steady floir mixes slightly wkore rapidly than the pulsating flow.
Howe-rer, the facts that the accuracy of the absolute levola of
pressure Beasuroment by the sampler value is not known, and
that tl.e measurenents of the steady flow values are approximate
to the extent that flow turbulence caused a nanometer water level
fluctuation of up to 0.5 inch of water would lead to a more rea-
sonable conclusion that the velocity nixini^ in the steady flow
case and the pulsating case differ in no appreciable degree,
consistent with the control e^.ercised in this investigation.

'M-Ltmh^w.

T\ It

- 5JC -

wx •>>

a\x

p

J.. . i

O.ol

a.x-^

!

hX *<•■_

■V

0.75

O.'jS

0.25

r "~

.,-tA*ft

WD±

B OC

i^Bovn! 2

'?

n

- 55 -

CQHCUJSIOMS ASD RSCOMMBNDATIONS
trar. ^«

t' With raspact to the aaapling -mlve« the oonolusions to

b« draim arei . .^..^r*. . ■« .

!• It oazi be utilised in invest igati one of this nature
In Its present oonfi juration, but at the ooet of oonaiderable
tiae expended in calibration and reoheoking of data.

2. The Talve is extremely inflexible. Its ran.;^e of
operation oould be extended and its aocuracy inor eased by elim-
inating the bearing action of the rotor and by protidin^ a neans

of cooling the rotor and oasing.

he

Tp 3. When properly calibrated and used vithin its

lltBltatiCDS it can pronride reprodaoible data, however, the ac-
euraoy of the absolute level of pressure neasursments is not
definitely known, and the effects of pulsation form and freq-
uency, and of t>ie pressure differential applied across the vav«,
upon the accuracy of neasurement could well be a subject of fur-
ther investigation.

With respect to the test equipment, it is recosmended
that a Bore flexible, simpler design patterned after that of

ilM

Forstall and Shapiro (c) in which the secondary flow is drawn
ttirough the test aection rather than blown through would be Mm
adaptable to the turbine test cell layout of the Ueohjinioal lio-

- as -

i:oa«e^o^^ vo»tl'ooa a;*'! bna b' ' »o bXcoo nocJii'ieqo

bn« baiBTcTliflo ^^liaqon ."

•pail tme itioI no lo a^oello wfi^ :;ns ^/twornl Yle:^ inxleb

^e *«rf:t -ci*:re bemo+ctur rr.^^9b tol . Icffxall s-ioa « ^arf*

•rf bXcwv i%uont{:^ n. indict nol^oea cfa»i 9i<d rfguonrfi

- 56 -

gineerin^ bepartnent, anc' wotild proTid© for smoother flow en-
tranca into the test section and p«rnlt 'noro aocurato detarmJ na-
tion of the velocity profile in the critical regions where mix-
ing is almost complete •

The sanpler valve must be redeslf^ned, if possible, or
a substitute method of measurin^^ varying pressures be applied
before tests beyond the scope of this preliminary investigation
oan be prosecuted to any de^ee of success.

'v«

In this investicstion of the mixing of a pulsating air
jet in a steady secondary airstrean it was found that*

1. There was no appreciable difference betwean the
velocity mix ng region of a cool, isothermal pulsating jet and
mixing region of a steady flow Jet of similar configuration, at
#, B«yiiolds number of 41,000 and ^ > 0.5, whan pulsations wera
foroad by regular interruption of the flow at 250 opm.

2. There was j;ood agreement with the findings of other
investigations previously made for the steady flow case thut:

(a) The fully normalised velocity profiles down-
stream of the potential core are of the same shape, irrespective
of the value of 5. and closely resemble a cosine curve.

(b) The centerline velocity, downetream of the

- S8 -

-n

•i las

ni.

I* 'J .'-'^ w'^

u»9;;te

9T

fl ^C

- 57 -

potential core, decays in direct proportion to th« value of -^

(o) The location of the end of the potential
core at the center line it closely defined by the enpirieal re-
lation

L ■ 4 ♦ 12 X

S. Ihe close agreement of the data of this investiga-
tion in the region w)iere pressure differences were large indicate
a reasonably good level of accuracy. The inability to accurately
define the outer ed^s of the jet, where t>ie pressure differences
are smaller indicate the ne«d for more closely controlled pulsed
flow investig;ation8 utilising measuring equipment more sensitive
than the mechanical sampling valve used in the experiment.

4. Based on the ratio of the Jet velocity in excess

of the secondary flow to the original jet velocity in excess of

the secundary flow. "*H* « the centerline flow was considered

"o-"8

SS% wlxed at an avera^^e iL • 36 for both the steady and pulsating
oases, was 6&^ alxad at an average •=• * 24, and was 45^ mixed at

X

an average ^ ■ 18. In both oases the steady flow jets appeared
to alx slightly sooner titan the pulsating jet, but the accuracy
of the data does not justify drawing a firm ooncluaion to that
effect.

- TS -

mis lO £01 (o)

•»t I*r >e»olo »1 «♦« >o Off* ;tB *tpi>

X §1 4 *• « .:

39or

- a;? Xi^iMmiU V 'is 'Ic isv©! iioo^^ \> - • .■■"

^fr "'^ " '•' bn« ,1*^ = ■ ,,.jL^ .^83 ojbw .bb^u-j

- 88 -

5. It is reoooawadsd that further invest lotions of
tM« nature be Biade to check the effects of variation in pulse
frequency, of pulsation forn, of velocity ratio^ /^ » and of
Reynolds nunber, upon the nature of the taixin^ region of a pul-
aating jet»

\S) *C ^^ ^* believed that the uae of i.lgh apead photography
coupled with bc>ilieren and/or shadowgraph flow visualisation
techniques W^^^t^, FI°^® * profitable avenue of investi^jation.

««iiA6> mJ^'i low

f

?«rt #U» M^r 19^

(9) Plov ItoMV*'''*' ^ 19^9. 1.5^.1C!.?. Pfs»r T««t Coda

• ■' /

• m^^ >*£ ;;ibae«otfc i.:JdO.

J., a i-qa.

- 8« -

•tfrjc: Tf co!:*«,-ter '>n 'o o& •ban ed oiud^an •ixii'

- 89 -

BIfiLIOGRAPHT

(1) "Report on the Investigation of i>e70 loped Turbulence",

L. ^andtl, N.A.C.A. T.M. #1231, September 1949.

(2) "The Transport of Vortioity and Heat Through Fluids in

Turbulent Motion", G, I, Taylor, ?roc« Roy* Soc.
1135, p. 685 and 702, 1932.

(3) "Calculation of Turbulent -ocpansion Processes", Walter

Tollmein, H.A.C.A. T.U. irl085, 1945.

(4) " Invest ii;;at ion of Turbulent Wixin^ He^^iwis Porned by Jets",

Arnold U. Kuethe, J.A.M., toI. 2, i?3 pp. 87-95,
Septenber 1935.

(5) "Isothermal and I«on-Isothernal Air Jet Investigations", V.

Cleeves and L. U, I. Boo Iter, Chen. bjig. Prog.,
vol. 43, p. 123, liarch 1947.

(6) "Uomentum and Mass Transfer in Coaxial Gas Jets", Valton

Forstall, Jr. and A. 11. bhapiro. Journal Applied
Meohanics, vol. 17, Ko. 4, i^eoenber 1950.

(7) "Gas Turbines for Aircraft", Gods^ and Young, p. 152,

UcCraw-nill, 194J.

(8) "Flame Stabilisation and Propogation in High Velocity Gas

Streams (100-400 fps)". A. C. Scurlock, MIT Guided
Missile Program, Report rl9, liSay 1948.

(9) Ploir Measurament, 1949, A.S.I/.f:. Pover Teat Code 19. 5j

4-1949.

(10) "The Relative Pressure Lrop Coeffioients for a Square Edged

Orifice in Steady and Pulsating FIov", £. K. Becker,
Master's Thesis, University of Minnesota, August 1950.

(11) "A Study of the Effect that Low hYequency i\ilsations llave

on Pressure Lrop Coefficients for a square Fudged Ori-
fice". Robert Y. YJong, Master's Thesis, University of
Minnesota, August 1951.

(12) "The ^ffeot of Pulsations on Plows of Oases", Horace Judd

and D. B. Phelay, A.S.M.K. Trans., vol. 44, 1922.

- 25 -

«t isK- " (e)

id. CI ai.
•^ S 4* (XI)

• SS9X «M .lov ,

- 40 -

strntio*

pw4.«

iiAiD^.r nrA4;«'.ir/D. .":

of

APPBIDIX

^COT'Cii "0 0*1.

- 0* -

- 41 -

i. -w HcftBurano LIST Of t]

D Hostl* dianetftr. Inches tmmm

L Axial distance from noszle exit, in diameters, of end of
potential core

p Pressure, psia or in. K2O

q iiynamic pressure, psl or in« HgO

r Kadius, inches

r,i liadiue, inches, wl.ere velocity is arithnetic average of
aecondan'^ and center line values at any x.

a Axial flow velocity at any point

X Axial distance fYom nozzle exit, inches

y lateral distance from nossle centerline, inches

subscripts 1

j Jet ^

0 Total as in p t naxlKUM as in qo or Uq*

p Priaary flow

• Statie aa in Pg} secondary flot? as in q^ or Ug.

Grmmk Letters >

A Differential value

^ Absolute Viscosity ft "sen ^

^ Density, ^

^ Ratio of secondary velocity to oenterllne velocity at — ■ 0.

- Lb '

Id

1 1 , It

I ai^S&pd

nfssc'? a

10 c

^ai-o^ssaiJ .11 ^jxxe cii;

lo

C 81 3C

c^n .

i i - dj

aerfofr alb laixi x

3».-v r ■. ■ . t^n ' T IS * '»'i f? r X

• qU 10 op nl a« f;

&l'

Wr

tS^ff f-I«>«lfBd

o

anf>!*.-^iai iB«<fi

• ^ • - ,i|oeI»V ^i:ix-iL...Ta{

;:.'-isv -1.^ irrnjia i'll^

dl

>^

' OJ \,JXOOi3V ^'i>

^
A

- 42 -

1* Air Flaw Measurement and Calculation

'" The orifioaa in the system have been Installed in ac-
cordance with A.S.l'.E* Code. The equation used to find the mass
flour vast

where

W « 0.668 Ag fETJ^^p

W • Mass flow in lb per sec.

^2 ■ Throat area in square in.

K - Flow coefficient

K - Area nultiplier for therBMkl expansion of the
orifice plate,

T • Empirical expansion factor

^ « Upstream density of flowing air

Af « ftressure drop across the orifice plate in pel

For a typical exaaple of the determination of the nass
flow with an orifica plate, see ejuinple 2, psge 7, rof . (9).

Calculation of Meynolds Number

2. The Reynolds aunber was oaloulated fron the following equation:

3* The natural frequency of the tube with one end closed is cool-

pated froo ti:e following equation}

a

f «

XL

- s^ -

-o» nf baX.

fljedOYa srfi fii aeofliio srfT

"O

octi

^A-v_U

Ij

,098 ^oq Tii iu v.c

-.'tOilW

raq

-?P • rf.hwl'>

Iv' l"/tr <- VJ

^.^'; u aA

as Ad on J iv ."■_- r j 8

j-t n .. «. r.

Xflo iq-^

«oXl

xrr

**oo f

■I. -sjaJLi-'Oiflo 3flw T'B»ar4ua abic.^

VI

ono r{;^±w ei

>^.

•.noiJi'-"''

- 43 -

TABLE X OK
CTCm CP imU. FULSITIIG FLOf 1

CYCLE OP DYMAMIC I'RKSSCKL, q, IN INCHES OF WiTER

^ , Distance from fiostle Center, inohes

Degreea 0

0.1

0.2

o.s

0.4

O.S

1.0 to 2.

.5 ,

10

15.70

15.15

14.85

14.10

11.85

9.70

3.55

,

20

15.80

15.30

15.00

14.10

11.95

9.75

3.40

f

30

15.60

15.10

14.80

13.95

11.90

9.G5

3.60

40

15.35

14.85

14.60

13.60

11.40

8.35

3.40

,

50

14.95

14.40

14.25

13.30

11.25

9.10

3.75

■)

60

14.50

13.95

13.80

12.80

10.80

8.65

3.60

)

70

14.20

13.65

13.40

13.00

10.55

8.50

3.55

30

13.80

13.25

13.05

12.20

10.30

8.30

3.75

90

13.50

13.00

12.75

11.90

10.00

8.20

5.55

100

12.85

12.30

12.15

11.30

9.40

7.70

3.50

110

12.60

11.90

11.75

11.00

9.20

7.65

3.40

120

12.06

11.65

11.30

10.50

8.60

7.00

3.30

130

11.40

10.85

10.70

9.85

8.10

6.50

3.25

liO

10.90

10.40

10.25

9.54

7.70

6.06

3.15

150

10.55

10.05

9.85

9.15

7.40

5.90

5.15

160

10.16

9.62

9.49

3.75

7.21

5.72

2.90

;

170

9.95

9.40

9.30

8.60

6.90

5.40

3.05

180

10.13

9.62

9.40

8.75

7.16

5.70

3.00

190

10.45

9.80

9.65

3.80

7.20

5.70

2.70

;

200

10,60

9.90

9.85

9.00

7.40

6.90

2.85

210

10.70

10.00

10.00

9.10

7.45

6.00

2.85

220

11.30

11.00

10.40

9.55

7.95

6.45

2.90

230

11.80

11.10

10.95

10.10

8.40

6.80

3.50

240

12.30

11.46

11.40

10.40

8.70

7.10

3.80

250

12.60

11.85

11.75

10.76

9.00

7.40

S.85

260

13.05

12.20

12.10

11.10

9.40

7.60

3.80

J

270

13.40

12.50

12.40

11.45

9.70

8. CO

3.75

230

13.90

13.00

12.85

11.85

10.00

6.20

3.70

290

14.10

13.20

13.10

12.10

10.10

8.40

3.60

)

300

14.50

13.65

13.40

12,20

10.30

8.45

3.55

»

310

14.90

14.00

13.90

12.80

10.80

8.70

3.70

)

320

15.10

14.45

14.30

13.20

10.90

9.03

3.60

1

330

15.30

14.40

14.40

13.25

11.10

9.10

3.45

340

15.35

14.55

14.45

13.40

11.40

9.40

3.55

350

15.50

14. GO

14.60

13.55

11.45

9.50

3.7

360

17.00

14.95

14.95

13.80

11.70

9.65

- e* -

-i^^CklL-'i

a

,T3Tn- -• ai.5S

1

a

5.C

0 a»»*qog

r.r. . 5

oT.e

X c.

r ^-

;l Of

COaCX

oe.s sv.e

OT.S
88. S

60. S
OG.S

i c

.e

.XX

. .i ^'^>. ..1.

.xX

if =:'>.sx

OSI

x

■x

.

X

.e ex. ex

Ci)I

ee.s

ovx

SI. CI

OoX

o«x

s

iS

^

OSS

. ex oe.ii

^rs

. •■ r??:.?i

Oi:^

X

OSS

r

Ods

I

ov$

I

OSf

b'^.v wt«j.x

oxe

0*6

■5
^.o5

- 44 -

TABLE II

FULSATIHG FLOU

CYCLE OF DTSAMIC Ffi£SSU££, q» IN IRCBBS OP WATER

Distance fron Sosxle Center, inches
^ Degrees 0.0 0.2 0.3 0.4 0.5 0.6 0.7 to 2.5

10

15.20

14.50

13.25

10.75

7.10

4.00

3.45

20

16.45

14.75

13.40

10.90

7.06

4.05

3.50

50

15.40

14.70

13.25

10.80

7.06

4.00

3.50

40

15.05

14.35

12.95

10.50

6.90

3.90

3.50

50

14.70

14.00

12.55

10.25

C.65

3.85

3.50

60

14.30

13.60

12.30

9.85

6.45

3.85

3.50

70

14.00

13.70

11.90

9.60

6.30

3.85

3.50

80

13.45

12.75

11.50

9.45

6.20

3.85

3.50

90

13.10

12.40

10.90

9.20

6.05

3.80

3.50

100

12.70

12.00

10.75

8.65

5.80

3.60

3.40

110

12.30

11.60

10.15

8.45

5.55

3.50

3.25

120

11 ,85

11.15

10.00

8.05

5.35

3.40

3.25

ISO

11.15

10.50

9.55

7.80

5.10

3.25

3.05

140

10.80

10.00

9i25

7.60

b.OO

3.26

3.10

150

10.35

9.70

8.70

7.25

4.80

3.05

2.95

160

10.00

9.30

8.55

7.15

4.70

3.00

2.95

170

9.70

9.10

8.20

6.85

4.60

3.15

3.00

180

10.00

9,20

8.40

7.10

4.70

3.50

3.40

190

10.15

9.45

8.35

6.95

4.65

3.45

3.30

200

10.20

9.50

8.30

6.85

4.55

3.50

3.20

210

10.35

9.65

8.45

6.90

4.55

3.55

3.10

220

10.60

9.90

8.G5

7.15

4.80

3.50

3.25

230

11.05

10.35

9.10

7.60

5.00

3.50

3.40

240

11.65

10.95

9.55

8.00

5.30

3.50

3.30

250

11.80

11.10

9.90

8.15

5.45

3.65

3.45

260

12.35

11.65

10.30

8.55

5.65

3.70

3.50

270

12.70

12.00

10.55

3.75

5.85

3.75

3.50

280

12.90

12.20

10.80

9.05

5.93

3.80

3.45

290

13.40

12.60

11.35

9.35

6.1;'5

3,80

3.50

300

13.80

13.10

11.50

9.40

6.25

3.85

3.45

310

14.10

13.40

11.90

9.80

6.40

3.85

3.50

320

14.30

13.60

12.00

10.05

6.40

3.80

3.45

830

14.50

13.80

12.55

ie.25

G.60

3.85

3.50

340

14.80

14.10

12.70

10.35

6.55

3.80

3.50

350

14.90

14.20

12.80

10.60

6.75

3.85

3.50

860

15.10

14.40

12.90

10.65

6180

3.85

3.45

II aauT

,p ,. ,iJi.aiii i IV -MivJiv/

. «5

8©r( c ni » "

3.S o& T.O 8,C S.C ^ ^^ S.G 0.0 a^OTts^

■%- :. o;,T RT.rr r^s.-r cs.M OS. SI 01

■ c

O^'.S SS.OI 3c. 0T.*«

05,5

Od.S

Ot:.^

d».

03.:-

ca.o

03.0

3^.8

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SG.S
36. S

OI.fi

OS.?;

dl.Ci

.11

. i I

c>; .

' ■ r

a . .

i.

es*G

(■■

b

0Y.3

wO * Vwk

CC^L

r-c.3

v.>C.-.-i

«?C.OI

OdI

CS.'i

cx.e

OT.e

OTX

0^,3

OS.R

OO.Oi

oei

:;S,t

ii'.e

21.01

OCX

Co. 3

c-i.e

OS. OX

iOOS

a^.G

ea.G

:^S.CX

OXS

30. S

''0

08 .OX

CSS

01. n

?,-:-. -^.i

30. IX

oes

uo.t

gC.OX

3D. XX

OI^S

C" , '

CX.ii

08.11

oes

C

so. II

sr.ai

CDS

\>

1 r

OT.SX

0?S

t

-

08. SI

OSS

G ■

;

Ofr.ex

ces

C. .

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08. 5X

ooc

c .

r

OX.H

or«

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cx.;.x

0»S

- 46 -

TABLE III

PULSATIKG FUM

CYCLE OF DYHAMIC P&£SSUKL» q, IN IBCHBS OP WATER

X

Distance from Nossl« Center, ^nehee

Degrees 0.0

0,1

0,2

0.3

0.4

0.5 0.8 to 2.5

10

14.10

13.60

12.60

9.95

7.50

5,00

3.45

20

14.25

13.85

12.70

10.00

7.50

5.05

3.50

30

14.20

13.75

12.65

9.95

7.50

5.20

3.60

40

13.90

13.35

12.30

9.70

7.25

4.95

3.45

50

13.60

13.10

12.05

9.60

7.10

4.95

3.55

60

13.20

12.65

11.60

3.10

6.70

4.80

3.55

70

13.00

12.35

.11.40

9i00

6.65

4.75

3,60

80

12.60

12.15

11.20

8.86

6.65

4.80

3.70

90

12.30

11.80

10.90

8.60

6.50

4.70

3.55

100

11.70

11.30

10.30

8.15

6.15

4.40

3.53

110

11.35

11.00

10.10

8.05

6.25

4.25

3.25

120

11.00

10.60

10.55

7.60

5.6b

4.10

3.20

130

10.35

10.00

9.10

7.05

5.20

4.02

3.10

140

10.00

9.65

8.80

6.70

6.00

3.90

3.10

150

9.70

9.30

8.55

6.55

4.80

3.69

3.00

160

9.32

8.95

8.21

6*45

4.70

3.40

3.00

170

9.00

0.60

7.90

6.10

4.45

3.28

2.95

180

9.25

8.95

8.30

6.50

5.10

3.50

3.00

190

9.10

8.70

7.90

6.10

4.61

3.50

3.00

200

9.25

8.85

8.00

6.30

4.80

3.59

3.00

210

9.40

8.95

8.10

6.30

4.80

3.42

2.79

220

9.94

9.51

8.62

6.85

5.25

3.80

3.06

230

10.35

10.00

9.05

7.20

5.40

4.10

3.31

240

10,70

10.25

9.30

7.40

5.80

4.20

5.30

250

11.15

10.75

9.75

7.70

5.85

4.20

3.49

260

11.45

11.05

10.05

8.05

6.20

4.50

3.50

270

11.90

11.40

10.30

8.25

6.35

4.70

3.61

280

12.30

11.75

10.65

8.50

G.50

4.80

3.50

290

12.45

11.90

10.80

8.80

6.45

4.75

3.51

300

12.80

12.25

11.10

8.70

6.60

4.85

3.50

310

13.25

12.75

11.50

9.10

6.75

4.90

3.56

320

13.40

12.95

11.75

9.25

6.96

5.05

3.80

330

13.85

13.06

12.00

9.40

7.00

5.00

5.55

340

13.^5

13.15

12.20

9.70

7.25

5.10

3.60

350

13.90

13.25

12.30

9.80

7.45

5.20

3.60

3G0

13.90

13.35

12.35

9.80

7.50

5.10

3.48

Ill MAMU

\..

U

G;.

J s

- 46 -
fgUM If

CYCLE OF DTXAUIC rai-:S8UKE, q, II INCHES OF WiTBR

DtitindU fron Noszle Centi^, inohae
Degrees 0.0 0,1 0.2 0.5 0.7 0.9 to 2.5

10

10.95

10.60

9.25

5.10

3.80

5.56

20

11.25

10.75

9.45

5.25

3.85

3.55

SO

11.00

10.65

9.40

5.35

4.00

3.70

40

10.80

10.55

9.10

5.10

3.80

3.45

SO

10.55

10.25

9.00

5.10

3.90

3.45

60

10,20

10.00

8.66

4.95

3.80

3.60

70

10.00

9.70

8.35

4.85

3.70

3.55

80

9.70

9.50

8.25

4.85

3.85

3.65

90

9.55

9.25

7.90

4.60

3.75

3.45

100

9.10

8.85

7.65

4.65

3.55

3.25

110

8.90

8.60

7.35

4.35

3.40

3.20

120

8.50

8.25

7.15

4.20

3.30

3.20

130

8.05

7.80

6.70

3.80

3.25

3.05

140

7.75

7.50

6.05

3.70

3.10

3.05

150

7.50

7.25

C.30

3.65

3.15

3.05

160

7.20

7.00

6.90

3.55

3.15

3.00

170

7.05

6.80

5.80

3.40

3.35

3.05

180

7.30

7.05

6.00

5.72

3.35

2.95

190

6*55

6.35

5.35

3.60

3.30

3.05

200

7.15

6.95

5.95

3.75

3.20

2.95

210

7.25

7.05

6.05

3.80

3.26

3.05

220

7.56

7.30

6.35

3.90

^ 3.85

3.25

250

8.05

7.80

6.75

4.10

3.45

3.35

240

8.30

8.05

7.00

4.25

3.60

3.40

250

8.55

8.35

7.25

4.50

3.75

3.45

260

8.85

8.65

7.45

4.50

3.65

3.65

270

9.10

8.95

7.80

4.70

3.80

3,65

280

9.36

9.20

7.95

4.80

3.95

3.60

290

9.50

9.35

8.05

4.85

3.85

3.45

300

9.90

9.60

8.30

4.85

4.00

3.65

310

10.26

9.85

8.50

4.95

4.10

4.70

320

10.40

10.30

8.90

5.10

4.15

4.45

330

10.56

10.30

d.95

5.25

4.10

3.50

340

10.66

10.45

9.10

5.30

4.15

3.55

360

10.85

10.50

9.20

5.30

4.15

3.65

360

10.90

10. G5

9.30

5.25

4.20

3.55

- Ov -

9L^k^: iO a.

zodoal ^f^tmO oXsscS laoil QociB&Bid

fi..'.

,0

9A.Z

cis.a

crCLB OF

- 47 -
TABLE Y
PULSATING FIOK
rC FRESSUEE, q, IH INCHES OF WATKK

X

Dlatanoe from llozzlo Center inches

De£p*««s 0.0 0.1

0.2

0.5

0.5

0.7

0.9 1.1 to 2.5

V

10

8.20

8.05

7.95

6.95

5.80

4,65

4.05

3.60

20

8.20

8.10

7.90

6.96

5.80

4.66

4.00

3.60

30

8.30

8.16

7.90

7,00

5.95

4.G5

4.05

3.65

40

8.U

7.95

7.70

6.86

5.76

4.50

4.00

3,60

50

7.85

7.70

7.70

6.66

5.66

4.50

3.90

3.60

GO

7.90

7.30

7.50

G.60

5.60

4.56

4.05

3.70

70

7.60

7.40

7.20

6.36

5.55

4.36

3.95

3.60

80

7.60

7.36

7.50

6.16

5.56

5.00

4.00

3.65

90

7.20

7.00

6.72

G.09

S.22

4.30

3.90

3.50

100

7.00

C.80

6.55

5.80

5.15

4.06

3.68

3.40

110

6.75

6.50

6.40

b,6S

4.90

4.05

3.80

3.30

120

6.50

6.30

6.10

5.50

4.76

0.90

3.53

3.50

150

6.35

6.10

5.90

5.35

4.60

5.75

3.50

3.20

140

6.10

5,86

5.85

n.l2

4.41

3.70

3.44

3.20

160

5.90

5.76

5.40

5.00

4.32^

3.52

3.30

3.00

160

5.66

5.00

5.15

4.86

4.25

3.50

3.25

3.00

170

5.31

5.10

4.75

4.51

3.96

3.40

3.10

2,90

180

5.60

5.40

5.07

4.75

4.20

3.50

3.25

5.00

190

5.40

5.20

4.90

4.60

4.10

4.10

3,20

2.95

200

5.50

v/ • bO

s.oo

4.59

4.20

3.55

3.25

2.90

210

5.50

5.26

5.15

4.30

4.30

3.40

3.23

3.00

220

5.80

5.68

5.35

5.00

4.40

3.71

3,30

3.10

250

6.10

5.90

5.70

5.16

4,55

3.85

3.50

3.20

240

6.27

6.02

5.88

5.25

4.60

3.90

3,59

3.30

260

6.70

6.40

6.20

5,60

4.90

4.11

3.70

3.45

260

6.85

6.66

6.35

5.75

5.10

4.20

3.80

5.6u

270

7.00

6.36

6.66

5.95

5.20

4.30

3.90

3.60

280

7.15

6.96

6.75

G.OO

5.35

4.40

3.90

3.60

290

7.30

7.10

6.95

6.16

5.40

4.46

3.31

3.60

300

7.50

7.30

7.05

C.30

5.45

4.40

3.90

3.50

310

7.75

7.50

7.30

G.40

5.60

4.40

3.85

3.50

320

7.73

7.60

7.34

G.50

5.55

4.40

3.90

5.60

»30

8.00

7.S6

7.50

6.70

5.70

4.35

3.95

3.66

340

8.15

7.96

7.70

G.70

5.70

-' . 50

3.95

3.60

350

8.13

7.96

7.70

6.80

5.36

4.60

4.00

3.55

360

8.25

8.06

7.90

G.90

5.95

..55

4,02

3.60

'■iij iiahUi.i i(ii tp I

r.i ji.xAt.i\i v> cucnrs

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- 48 -

TABLE YI

PULSATING PLOf

CYCLii OF DYKAKIC . iE, q, IN IMCHSS CP WATIE

X

D • 21
Distance fron tiozslo Center, Inches

l^e^ees 0.0 0.6 1.2 l.S 1.5 to 2.5

10

5.02

4.50

4.00

3.80

3.60

20

5.18

4.65

4.15

3.95

3.65

30

5.23

4.70

4.20

4.00

7.70

40

5.02

4.65

4.15

3.95

3.50

50

4.95

4.50

4.10

3.90

3.50

60

5.00

4.50

4.10

3.90

3.70

70

4.85

4.40

4.00

3.80

3.65

30

4.80

4.26

3.85

3.75

3.75

90

4.70

4.15

3.85

3.75

3.65

100

4.47

4.05

3.75

3.75

3.46

110

4.30

3.95

3.65

3.55

3.50

120

4.25

3.85

3.55

3.45

3.40

130

4.20

3.85

3.55

3.45

.-5 .35

140

4.15

3,75

3.45

3.35

3.30

160

4.1

3.75

3.45

3.35

3.50

160

4.0

3.60

3.40

3.30

3.20

170

3.95

3.60

3.30

3.10

3.10

180

4.05

3.50

3.40

3.30

3.30

190

3.95

3.40

3.30

3.20

3.20

200

3.85

3.60

3.40

3.50

3.10

210

4.05

3.40

3.30

3.20

T.20

220

4.15

3.40

3.40

3.30

3.50

230

4.2

3.50

3.30

3.20

3.20

240

4.06

3.75

3.50

3.40

3.40

250

4.20

3.75

3.60

3.50

3.50

260

4.40

3.75

3.75

3.65

3.55

270

4.66

4.00

3.75

3.65

3.65

280

4.65

4.10

3.80

3.70

3.50

290

4.75

4.30

4.00

3.80

3.65

300

4.80

4.40

4.00

3.80

3.50

310

4.95

4.66

4.05

3.85

3.70

320

4.90

4.60

4.10

3.90

3.50

330

4.95

4.45

4.05

3.85

3.65

340

5.08

4.56

4.16

3.96

3.65

9t0

5.18

4.70

4-«eo

4.00

3.70

tk>

5.18

4.70

4.20

4.00

3.50

e 9j I y !T :

3I>.S

Oo*'^

- 8* -

XS -71

018

- 49 -
TABLE VII

puLSATisG rum

CTCU OF DTSAKIC FRE8MK, q, IN IfiCHKS OP WATEK

F • 24^

Ms

tance from Hotz

la Center, inches

0.0

Degrees

0.2

0.4

0.8

1.0

1.4

1.6 to 2.5

10

4.75

4.60

4.50

3.96

3.70

3.66

20

4.75

4.60

4.20

4.05

3.75

3.66

SO

4.70

4.50

4.20

3.95

3.75

3.55

40

4.60

4.55

4.00

3.85

3.70

3.46

60

4.70

4.50

4.10

4.05

3.85

3.60

60

4.80

4.60

4.20

4.05

3.90

3.76

TO

4.80

4.60

4.20

4.20

4.00

3.75

80

4.76

4.55

4.20

4.10

3.90

3.75

90

4.60

4.25

4.05

4.05

3.85

3.65

100

4.55

i.20

3.86

3.85

3.65

3.45

110

4.25

4.20

3.90

3.90

3.75

3.55

120

4.15

4.15

3.75

3.75

3.55

3.35

130

4.15

4.10

3.76

3.66

3.55

3.40

140

4.10

4.05

3.70

3.65

3.45

3.25

150

4.00

4.00

3.66

5.65

3.45

3.25

160

5.9

3.95

3.46

5.65

3.40

3.25

170

5.90

3.85

5.55

5.60

3.20

3.20

180

4.00

3.90

5.40

5.50

3.40

3.15

190

5.90

3.85

3.50

3.50

3.40

5.15

200

3.80

3.70

3.50

3.50

3.40

3.16

210

4.00

3.80

5.55

5.60

3.50

3.16

220

4.10

3.95

3.76

3.70

3.60

3.25

250

4.15

3.85

3.55

5.55

3.45

5.20

240

4.0

3.95

5.65

5.66

3.55

3.25

260

4.15

4.20

3.85

5.80

3.65

3.40

260

4.50

4.20

3.95

3.90

3.75

3.50

270

4.60

4.25

3.95

5.90

3.75

3.50

280

4.40

4.20

3.86

5.80

3.70

3.45

290

4.55

4.25

4.00

5.95

3.80

3.55

300

4.05

3.86

4.06

4.00

3.90

3.60

310

4.60

4.55

4.20

4.05

3.90

3.66

520

4.65

4.40

4.06

4.00

3.95

3.60

530

4.60

4.25

4.10

4.00

3.80

3.60

540

4.65

4.40

4.05

4.00

3.80

3.60

560

4.70

4.50

4.20

4.05

3.85

3.75

560

4.75

4.55

4.25

4.16

3.75

3.75

csy

Si^ZJ

li

Y^

-fi,a i!u aaHOtti r.A ^p t.;i.^. .«, ^iJiAara "^ sjdtd

X

.0

.* c

ex.

► \» V

- 50 -
TABLE YIII
PULSATIHG FLOPr
CYCLE OP DYNAMIC PRESSURE , q, IH INCHES OF WATHl

|-"i

Distance fron Koxfle Center, inches
^^

Decree 0.2 0.9 1.5 1.7 to 2.5
0.4

10

4.25

3.85

3.80

3.70

20

4.40

4.00

3.85

3.75

30

4.25

3.85

3.75

3.60

40

4.15

3.75

3.65

3.55

50

4.25

3.85

3.75

3.70

CO

4.40

4.00

3.90

3.80

70

4.40

4.00

3.90

3.85

80

4.30

4.00

3.90

3.80

90

4.05

3.75

3.65

3.75

100

3.95

3.75

3.65

3.55

110

3.95

3.75

3.65

3.50

120

3.85

3.75

3.65

3.40

130

3.85

3.70

3.60

3.40

140

3.75

3.65

3.55

3.30

150

3.70

3,65

3.55

3.30

160

3.70

3.60

3.50

3.30

170

3.70

3.60

3.50

3.20

180

3.60

3.50

3.40

3.20

190

3.50

3.40

3.30

3.20

200

3.35

3.25

3.15

3.20

210

3.55

3.45

3.35

3.20

220

3.75

3.65

3.55

3.40

230

3.70

3.60

3.50

3.25

240

3.75

3.60

3.50

3.30

250

3.95

3.75

3.65

3.50

260

4.00

3.80

3.70

3.50

270

4.05

3.85

3.75

3.60

280

4.00

3.80

3.76

3.50

230

4.05

3.85

3.75

3.60

300

3,60

3.40

3.30

3.70

310

4.20

3.90

3.80

3.75

320

4.20

3.90

3.80

3.70

330

4.10

3.80

3.70

3.70

340

4.20

3,80

3.70

3.70

350

4.30

3,90

3.80

3.76

380

4.30

3,90

3.80

3.75

7i

.0

^ *i . Ok,

Oc .

:uii

it.

OS

:r.L nn»;

- 51 -
TABLS IX

puLsmerLOi

CYCU. OK DYNAMIC PRBSSURE, q, IK INCHES OF WATKR
Distance from liossle Center, inches

oTo

Degree 0.2 0.7 1.3 1.8 to 2.5
0.4

10

4.25

4.05

3.85

3.70

20

4.20

4.00

3.80

3.75

30

4.20

4.00

3.80

3.60

40

4.00

3.80

3.70

3.55

50

4.05

3.85

3.75

3.70

60

4.15

5.95

3.86

3.80

70

4.20

4.00

3.90

3.85

80

4.20

4.00

3.90

3.80

90

4.05

5.85

3.76

3.75

100

3.85

3.75

3.65

3.55

110

3.90

3.80

3.70

3.55

120

3.75

5.65

3,55

3,40

130

3.75

3. 05

3.S5

3.40

140

3.70

5.60

3.50

3.30

150

3.60

5.60

5.50

3.30

160

3.50

3.50

3.45

3.30

170

3.55

3.50

3.40

3.20

180

3.40

5.55

3.30

3.20

190

3.30

3.25

3.26

3.20

200

3.30

3.25

3.20

3.20

210

3.55

5.45

3.35

3.20

220

3.75

5.65

3.55

3.40

230

3.55

5.45

5«55

3.25

240

3.60

5.50

3.40

3.30

250

3.85

5.70

5.60

3.50

260

3.95

5.85

3.75

3.60

270

3.95

3.85

3.75

3.60

280

3.85

3.75

3.70

3.50

290

4.00

5.90

3.80

3.60

300

4.05

5.95

3.75

5.70

310

4.15

3.95

3.75

3.75

320

4.05

3.90

3.70

3.70

330

4.10

5.90

3.75

3.70

340

4.05

5.95

3.75

3.70

350

4.20

4.00

3.80

3.76

360

4.25

4.05

3.80

3.75

- i« -

OS ■ -r

S,S ->:-

.1

^1

On

0.:

o

c:
C
0..

c

c

c\

ev.
cv,
ov

CT
3Y.£

or

OY.S 05^1

- 58 -

TABLE X
MA-TTT FVUanm plot -?f3PTL»
CTCLK CP DYNAMIC PRESSURE, q, IK ITICKES OF WlTBl

i v^

Degree

^-39

V.9X

- 40

3.70.

20

^0 w • ^^

3.75

SO

S.60

40

3.55

50

3.70

60

3.80

TO

3.86

80

8.80

90

3.75

100

3.55

110

3.60

120

3.50

ISO

3.40

140

3.30

150

3.30

160

S.SO

170

S.20

180

3.20

190

3.20

200

3.20

210

3.20

220

5.40

250

3.25

240

3.30

250

3.50

260

3.60

270

3.60

280

3.50

290

3.60

300

3.70

810

3.75

320

3.70

330

3.70

340

3.70

350

3.75

360

3.75

L
Vf 4«t ^.78

-^ .78
5,T6

.'3-75

- se -

es « ~

9 ST; 0

01

OS

OS

dd.S

€t»£

Cr.r

Ud.^

-.'U

3t.C

oe

68, ^

cox

oil

rs£

31

os.s

OS. 5

CCI

- 55 -

TABLi. XI

MAXIXDM LT]1AUIC nOttVBB FRQPILS

q, INCHES OF WlTER

PttUatlng J«t

i

5

5

9

12

21

24.5

27.6

30

39

0

15.8

15.45

14.25

11.25

8.3

5.2

4.75

4.4

4.2

3.75

.1

15.3
15.

14.75

13.85
12.7

10.75
9.25

8.1

4.75

4.4

3.76

.2

7.9

4.4

4.2

3.76

.S

14.1

13.40

10.0

G.95

3.76

.4

11.96

10.9

7.5

4.6

4.4

4.2

3.76

.5

9.75

7.06

5.05

5.25

5,8

5.75

•6

4.05

5.60

3.76

.T

3.5

3.85

4.66

4.0

3.75

• 8

3.5

3.5

4.65

4.2

3.76

.9

3.5

3.5

3.55

4,0

4,0

5,76

1.0

3.4

3.5

3.5

3.55

3.75

4.05

5.76

1.1

3.4

3.5

3.5

3,55

3.6

3.75

1.2

3.4

3.5

3.5

3.55

3.6

4.15

3.76

1.3

3.4

3.5

3.5

3.55

3.6

3.95

3.8

3.76

1.4

3.4

3.5

3.5

3,55

3.6

3.75

S.75

1.5

3.4

3.6

3.5

3.56

3.6

3.65

3.8

3.75

1.6

3.4

3.5

3.5

3.55

3.6

3.65

3.65

3.75

1.7

3.4

3.5

3.5

3.55

3.6

3.65

5.75

3.75

1.8

3.4

3.5

3.5

3.55

3.6

3.65

3.65

3.76

3.76

3.76

2.5

3.4

3.5

3.5

3.55

3.6

5.65

5.65

3.76

3.75

3.76

\?

65 OZ 8.TS d.J^S IS il

r;7.S S;« K#

av.E

3V.C O.N

8.5

'-I.

3Kai

3.31

0

-

I.

'- •

1. ,

.il

#.

r

3.
3.

i> • L>

'j* •

9.^.

e.

.

^•S

O.L

.

K T

I.i

S.I

CO

i- • c>

k.l

?.S

^.5

a. I
.1

,

3.S

- 54 -

TABU. XII
.MUUHOM DYIIAmC i'Uz^ijbiii PROPILS

q, mowtt (V mm

Pulaatlnc Jet

$

f°

3

5

9

12

21

24.5

27.5

30

0

9.95

9.70

9.0

7.05

5.31

3.95

3.90

3.7

3.65

0.1

9.4

8.6

6.8

5.1

0.2

9.3

9.10

7.9

5.8

4.75

3.7

•«

0.3

8.6

8.20

6.1

4.51

A

0.4

6.9

6.35

4.45

3.96

3.85

3.7

0.5

5.4

4.6

3.23

3.4

.4

0,6

3.16

'>4

0,7

3.00

3.15

3.4

3.5

4

0*8

3.00

2.95

3.6

3.65

0i9

3.00

2.95

3.05

3.1

3.6

1.0

3.05

3.00

2.95

3.05

3.50

1.1

3.05

3.00

2.95

3.05

2*9

»«4

1.2

3.05

3.00

S.95

3.05

2*9

3.3

',4

1.5

3.05

3.00

£.95

3.05

2.9

3.1

3.4

-4

1.4

3.05

3.00

2.95

3*05

2.9

3.1

3.2

3.5

.4

1.5

3.05

2.00

2.95

3.05

2.9

3.1

3.2

JL

1.6

3.05

3.00

i.95

3.05

2.9

3.1

3.2

1.7

3.05

3.00

£.95

3.05

2.9

3.1

3.2

3.2

1.8

3.05

3.00

£.95

3.05

2.9

3.1

3.2

3.2

5.2

2.5

3.05

3.00

2.95

3.05

2.9

3.1

3.2

3.2

3.2

- #3 -

'r'?A",T "^ 2t"*?:-T

rhJaelLr^

Si

(j 9 X Y

3ii,t T.s oe.s

3.C

i.r.

w «

".-•

3V.^
IS.

q ^

v.s

S8.S

se.

a.s

OG.o

j«l^« «i/

.0

V ,

>*J

^•0

'»,

.?.

3,0
^.0

5.r. 6«s

s.s s.s s.s x.s e.s no.

o.i

, *.!

. 5.1

. a,x

.^

Y.I

. , 8.1

uO.ci

gO.S d«S

- 68 -

TABLE XI 11

unuin

MT -TATE LYHAinc rii;SSliEE PEOPILB

4, INCHES OF WATER
4, Lacium or waiar

Piilsatini^ Jet

z

X

1

i

^ «

C °

3

5

9

12

21

24.5

27.6

30

39

0

11.4

lia5

10.35

8.06

6.35

4.20

4.15

3.85

3.75

3.4

0.1

iO.85

10.0

7.8

6.1

3.4

0.2

iO.7

10.5

9.1

6.7

5.9

4.15

3.4

0.3

9.85

9.55

7.05

5,35

3.4

0.4

8.10

7.8

5.20

4.10

3.85

3.75

3.4

0.5

6.50

5.10

4.02

5.8

4.60

3.4

0.6

3.25

3.25

3.4

0.7

3.25

3.20

5.4

3.75

S.G5

3.4

o.a

3.25

3.20

3.20

3.85

3.75

3.4

0.9

3.25

3.20

3.20

5.25

3.50

3.7

3.4

1.0

3.25

3.20

3.20

3.25

3*65

3.4

1.1

3.25

2.20

3.20

3.25

3.20

3.4

1.2

3.25

3.20

3.20

3.25

3.20

3.55

3.4

1.3

3.25

3.20

3.20

3.25

3.20

3.45

3.55

3.4

1.4

3.25

3.20

S.20

3.25

3.20

3.55

3.4

1.5

3.25

3.20

3.20

3.25

3.20

3.S5

3.6

3.4

1.6

3.25

O.20

3.20

3.25

3,20

3.35

3.4

3.4

1.7

3.25

3.20

3.20

3.25

3.20

3.35

5.4

3.4

3.4

1.8

3.25

3.20

3.20

3.25

3.20

3.35

3.4

3.4

3.4

5.4

- 32 -

5STf

-^r ''^i-^-iT

c^eL 3«l.:t»<

ee

0

a a

K8

ST.

.5

til.^

os.^

ds.d

ciO,t' He.

>.

rr

C

K8

X.B

I.O

KS

ei.j^

e.3

1

• -J.

s.o

>.S

6S.e

^8,

,e

s.o

^•S

8V.

.5

01.^

3

*.o

KS

or.

^.0

^.5

.0

c»

t.c

r • w

ev.s

Cu.o

.

'-\0

^aO

V.5

oe.:.

dP.

A

#.e

la.s

Gl.

».e

os.s

an.c

.i

^.s

sa.s

0£.£

es.5

f
• a.

».£

?.3.£

2^.0

OS.?

d.i .

>.S

36. r

^ . .

.- ^

i^.x

KS

D,^

-

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i' . I

^

i-^i

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co.C

T.I

i ,

^.'■.

3?.:^

8.1

- 56 -

TABLI-: XIV
DTIAUIC ISKSan PROFILE
Steady Flam - Internediato Value
q, inches of water

§C0 3 5 9 12 16 21 24.5 27.5 30

0 11,4 10.7 10.3 7.6 5.9 4.3 3.4 3.2 2.95 2.9

0.1 11.3 10.6 9.8 7.3 5.9 4.2 3.4 3.15 2.95 2.9

0.2 10.7 10.2 6.5 5.4 4.2 3.35 3.10 2.9 2.9 .ZB

0.3 9.4 9.1 C.2 6.2 4.C 4.1 3.2 3.1 2.9 2.85

0»4 7.1 6.1 4.6 4.8 4.2 S.9 3.1 3.0 2.9 2.7

0.5 5.9 3.7 2.9 3.9 3.5 3.4 3.0 2.95 2.85 2.65

0,6 2.3 2.5 2.4 3.4 3.0 3.2 2.9 2.90 2.8 2.6

0.7 2.2 2.3 2.3 2.9 3.0 2.85 2.75 2.6

0.8 2.2 2,3 2.3 2.6 2.7 2.9 2.7 2.8 2.7 2.6

0.9 2.3 2.3 2.3 2.5 2.6 2rr 2.7 2.7 2.7 2.6

1.0 2.3 2.3 2.3 2.4 2.5 2.6 2.6 2.6 2.6 2.6

1.1 2.3 2.3 2.3 2.4 2.4 2.6 2.55 2.55 2.6 2.5
1*2 2.3 2.3 2.3 2.4 2.4 2.5 2.5 2.45 2.55 2.45

1.3 2*3 2.3 2.3 2.4 2.4 2.5 2.4 2.4 2.5 2.45

1.4 2.5 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.45 2.45

1.5 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.45

1.6 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.45
2.0 2.3 2.3 2.3 2.4 2.4 2.4 2.4 2.4 2.4 2.45

« as -

ei:

01

•i ^.IX 0

?.s

I.O
£•0

. .)

- 57 -

TABIZ XV

Lin«8 of Conatant ^"i*^..
liftxiBBim Value, ?ul«atinc Flow

4\^^' .057 .1 .2 .3 .4 .5 .6 .7 .8 .9

«— »>p^— ii I 111. Ill ....I I

0 .45 .40 .96 .28

S .58 .54 .51 .49 .45 .42 .39 .38 .30 .22

5 .60 .52 .46 .40 .35 .31 .26 .21 .15
9 .65 .53 .59 .35 .26 .18 .08

12 .90 .68 .50 .39

21 1.22 .72

24.5 1.08

27.5 .90

30 .70

- Vd -

V^

■7 T r -" ~

seniJ

. .;^, iiisj.' . .■j;'Ai:'v ;."\jr;i jvj»..

— /*

:5.

51. IS.

•

«

'.•."* •

s*# ^' ' •

IG.

t»C. .

-r-J.

ci

OS.

IS,

ee.

•

di^.

2d.

Od.

S

80.

■- J- •

DS.

* ■ - «

25.

se.

3S.

9

'•

08.

8d.
ST.

SS.I

SI

IS

cr

^^

OT,

OS

- 58 -

lABLI:. XVI

1 Linea of Con«tant ^"^
MBimun Value, Pulsating Flow

J> \ ^o^

- \ V = -^ '^ •^ 'S •* -S .6 .7 .8 ,9

0 .48 .43 .38 .33 .28 .21

8 .56 .53 .51 .48 .45 .42 .35 .29 .25 .15
6 .51 .44 .40 .36 .31 .27 .24 .20 .12

9 .52 .45 .36 .27 .20 .12
12 .72 .50 .30 .10

21 1.14 .52

24.6 l.SS .40

27.5 1.57

SO 1.50

- sa -

JII£wi-

c.:,ald

,i9yI»V nwniul"

;'C. i >v ' ~

as:..

9

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^^.

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ae

21,

OS.

^s.

vs.

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D5.

o>.

^«

id

SI.

OS.

vs.

01.

OS.
Of.,

05.

se

04>.

A

c

8

a

e

SI

. \ S

Co..

C£

- 69 •

TABLE XYII

Lines of Constant ***»
Intarcwdiste slue. Pulsating Flow

low

F

iO .04 .1 .2 .3 .4 .5 .6 .7 .8 .9

.48 .44 .40 .35 .30 ,19

3

.55

.60

.53

.49

.4G

.42

.40

5

.56

.50

.48

.42

.38

.34

.29

9

.59

.51

.44

.36

.29

.21

.14

12

.93

.75

.59

.39

.20

21

1.35

1.10

.23

24.5

1.55

.93

27.5
30

1.66
1.73

1.15
.88

V> • >^4

lactnl

d

Oik*

81.

:..i

is

3I«X do«x 6«Vi

- 60 -

XVIII

Lines of Coaastant ^"^ .
Intoraedlato Valuo, Staady Flow

-\ V'^16 •! •* •* •♦ -S .« .7 .8 .9

0 .48 .42 .38 .92 .29 .22

S •88 .52 .47 .43 .39 .55 .32 .27 .23 .14

5 .67 .58 .52 .46 .39 .32 .25 .17 .11

9 .87 .62 .48 .59 .50 .21

12 1.0 ,54 .40 .24

21 1.19

24.5 1.26

27.5 1.35

30 1.4

') lO £

V

1;

0

Xi

ta.

d» Yd.

'v i* e

oX

OV>*L ?.4t2

uo* « 'w* I .

d^*i QZ

• 61 -

TABLE Z2Z

q-qi

Lines of CoBotwit

^-Q»

a-<i

iJftxiBun VmlxM, &tM(fy flm

iXvj

• 1 .2 »S .4 »6 .G .7 .8 .9

0 ,45 »40 .35 .SI .26 .21

S mSfi .50 .46 .42 ,59 .95 .31 .27 .23 .16

• .9% .60 .62 .45 .39 .38 .25 .15

f .93 .63 .52 .42 .32 .10

12 1.02 ,6Q .43 .23

21 1.06 .24

24.5 I.IS

27.6 0«96

30 0.80 'i

'?.

6

4.^

- 62 -

TABLE ZX
CESTBRLIHE VALUES OF VELOCITY
(a) Steady Flam, intermediate valuo

g q-q* 9°-q. ^ ^,

0 9.0 9.0 1.0 1.0

8

8.3

9.0

ft

7,9

9.0

9

5.2

9.0

12

3.6

9.0

21

1.0

9.0

24.5

0.8

9.0

27,5

0.55

9.0

50

0.50

9.0

.925

.963

.380

.940

• 580

.762

.390

.625

.116

.340

.069

.298

.061

.247

.055

.234

(b) Pulaed Flow, interriOdiate value

0 8.05 8.05 1.0 1.0

s

7.80

8.05

.370

.985

6

7.00

6.05

.870

.935

9

4.70

8.05

.586

.765

12

3.00

8.05

.370

.610

21

0.85

8.05

.105

.324

24.5

0.80

8.05

.099

.310

27.5

0.50

8.05

.062

.249

30

0.40

8.05

.050

.224

- s^ -

n

..wl*^ VbM9&Z {»)

est.

USB*

Xdo.

X

;,

21

r

n

0

8. £

J

2. \^

0

Ci

sjjIjbv e

e»v.

OYb.
£83.

0

uO\J»

<;'-■<

- 63 -

TAfiLL XXI
VOUULIZED VELOCITT FSOFILES

1-12

(a) Steady Flow, Inteni»diat« Value: !!■ « 0.49 ^r^ « 1.1

i

q

q-q.

qo-qa

r

0

5.9

3.5

1.0

1.0

0 ..

0.1

5.9

3.5

1.0

1.0

0.184 5

0.2

5.4

3.0

0.855

0.925

0.37 4

0.3

4.6

2.2

0.63

0.7S5

0.55

0.4

4.2

1.8

0.515

0.718

0.73

O.S

3.5

1.1

0.315

0.56

0.92

0.6

3.0

0.6

0.171

0.413

I.IS

0.7

0.8

2.7

0.3

0.086

0.293

1.49

0.9

2.6

0.2

0.067

0.239

1.67

1.0

2.5

0.1

0.0285

0.169

1.66

1.1

2.4

0

0

2.04

(b) Pulsed Flow: 7^ « 0.575 , r^ ■ 1.1

a.te

0 6.35 3.15 1 1 0

0.1 6.10 2.90 0.923 0.96 0.159

0.2 5.9 2.7 0.855 0.925 0.317

0.3 5.35 2.15 0.683 0.815 0.475

0.5 4.6 1.4 0.445 0.666 0.790

0.7 3.75 0.55 0.175 0.418 1.10

0.9 3.50 0.30 0.095 0.308 1.42

1.1 3.20 0 0 0 1.74

- r.? -

o**^

"iulaV dd-BxJjaimei-iI ♦vJoX'-i ^«©;fv <a}

sP"^

i

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c

o. . r

IVX.O

68S0.C
0

ij •

0

5.5

I.C

0,t

X- • <J

'"* l'

s.s

d.^

■ .

8.1

s.^

i»X

«,s

n.o

O.-T

T.O

• -■ • *-

\ » a

8.0

s^o

d.S

y.o

I.O

d.S

o.x

■^

'.S

r r

•t . 5T3,

n - .

'oXI

:3

0

X

X

3X.5

de.d

0

.0

SS6.0

oe.s

ox .a

x.o

■ X • . '-

wi^.. .0

8d8.0

Y.S

e.8

s.o

av^.o

SXB.O

588.0

3X.S

as.s

s.o

OCT.O

aaa.o

3^1^.0

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8.>

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8X».0

oTX.O

?.e.o

er.s

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80S.0

aeo.o

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05.5

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0

0

0

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x.x

- 64 -

TAMU xxn

RCmiLIZXD TBLOeXTT IMTZUBI

il . 21

D

?

q

r^

r

0

3.4

1.0

1.0

1*0

0.0

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3.4

1.0

1*0

1.0

0.11

•8

3.55

0.95

0.95

0.976

0.28

•S

S.2

0.80

0.80

0.805

0.84

•4

sa

0.70

0.70

0.886

0.46

»8

3.0

0.60

o.ao

0.775

0.87

•6

2*9

0.60

0.50

0.706

0.68

•8

2.7

0.30

0.30

0.65

0.91

1*0

2.a

0.20

0.20

0.45

1*14

1.1

2.65

0.15

0«15

0.59

1.28

1.2

2*50

0.10

0.10

0.31

1.88

1.8

8.4

0

0

0

1.47

(b) PulB«d Flew )

vt'-

,C8 ^ To •

1.5

0

4.20

0.96

1

1

0

0.8

S.8S

0.80

0.527

0.726

0.69

1*2

8.65

OJtO

0.2U

0.460

1.04

1*8

3.45

0.06

0.0527

0.229

1.128

1*6

3.85

0

0

0

1.3

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Fig, 2-a Control joanel for engine operation

Fi^, 2-b Engine, blov/er, at'^ rnanifolu
(The test set-up shown is not part of this experiment)

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Thesis

Beae

1G258

Burton

m

Preliminary investigation of
the mixing of a ouls^tin^ air iet in
a steady tggoMary alrflfw "^ °

DATS DUE

BORHOVEB'S :TA)S